# COMPOUND ANGLE PRACTICE QUESTIONS FOR GRADE 11

Compound Angle Practice Questions for Grade 11 :

Here we are going to see some practice questions on based on compound angles.

## Find the Value of Sin x Plus y When Sin x and Cos y are Given - Example problem

(1)  If sin x = 15/17 and cos y = 12/13 , 0 < x < π/2 , 0 < y < π/2, find the value of

(i)   sin(x + y)         (ii)   cos(x − y)          (iii)   tan(x + y).

Solution

(2)  If sin A = 3/5 and cos B = 9/41 , 0 < A < π/2, 0 < B < π/2, find the value of (i) sin(A + B) (ii) cos(A − B).

Solution

(3)  Find cos(x − y), given that cos x = −4/5 with π < x < 3π/2 and sin y = −24/25 with π < y < 3π/2.   Solution

(4)  Find sin(x − y), given that sin x = 8/17 with 0 < x < π/and cos y = −24/25 with π < y < 3π/

(5)  Find the value of (i) cos 105° (ii) sin 105° (iii) tan 7π/12

(6)  Prove that (i) cos(30° + x)  =  (√3 cos x − sin x)/2

(ii) cos(π + θ) = −cos θ

(iii) sin(π + θ) = −sin θ.     Solution

(7)  Find a quadratic equation whose roots are sin 15° and cos 15°.    Solution

(8)  Expand cos(A + B + C). Hence prove that

cosAcosB cosC = sinAsinB cosC + sinB sinC cosA + sinC sinAcos B, if A + B + C = π/2     Solution

(9)  Prove that

(i) sin(45° + θ) − sin(45° − θ) = √2 sinθ.     Solution

(ii) sin(30° + θ) + cos(60° + θ) = cos θ.       Solution

(10)  If a cos(x + y) = b cos(x − y), show that (a + b) tanx = (a − b) cot y.    Solution

(11)  Prove that sin 105° + cos 105° = cos 45

(12)  Prove that sin 75° − sin 15° = cos 105° + cos 15°Solution

(13)  Show that tan 75° + cot 75° = 4.   Solution

(14)  Prove that cos(A + B) cosC−cos(B + C)cosA = sinB sin(C−A).   Solution

(15)  Prove that sin(n + 1)θ sin(n − 1)θ + cos(n + 1)θ cos(n − 1)θ = cos2θ, n ∈ Z.   Solution

(16)  If x cos θ = y cos (θ + 2π/3) = z cos (θ + 4π/3), find the value of xy + yz + zx.    Solution

(17)  Prove that

(i) sin(A + B) sin(A − B) = sin2 A − sin2 B       Solution

(ii) cos(A + B) cos(A − B) = cos2 A − sin2 B = cos2 B − sin2 A

Solution

(iii) sin2(A + B) − sin2(A − B) = sin2Asin 2B     Solution

(iv) cos 8θ cos 2θ = cos2 5θ − sin2 3θ     Solution

18. Show that cos2 A + cos2 B − 2 cosAcosB cos(A + B) = sin2(A + B).   Solution

19. If cos(α − β) + cos(β − γ) + cos(γ − α) = −3/2, then prove that  cos α + cos β + cos γ = sinα + sinβ + sinγ = 0.  Solution

(20)  Show that

(i) tan(45° + A)  =  (1 + tanA)/(1 − tanA)    Solution

(ii) tan(45° − A) =   (1 + tanA)/(1 − tanA)   Solution

(21)  Prove that cot(A + B) = (cotAcotB − 1)/(cotA + cotB)  Solution

22. If tan x = n/(n + 1) and tan y = 1/(2n + 1) , find tan(x + y).  Solution

(23)  Prove that tan (π/4 + θ) tan (3π/4 + θ)  =  −1.  Solution

(24)  Find the values of tan(α+β), given that cot α = 1/2, α ∈ (π, 3π/2) and sec β = −5/3, β ∈  (π/2, π).   Solution

(25)  If θ + φ = α and tan θ = k tan φ, then prove that sin(θ − φ) = (k − 1)/(k + 1) sin α.  Solution After having gone through the stuff given above, we hope that the students would have understood "Compound Angle Practice Questions for Grade 11"

Apart from the stuff given above, if you want to know more about "Compound Angle Practice Questions for Grade 11".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 