# BASIC TRIGONOMETRIC IDENTITIES WORKSHEET

Basic Trigonometric Identities Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on basic trigonometric identities.

Before look at the worksheet, if you would like to learn about basic trigonometric identities,

## Basic Trigonometric Identities Worksheet - Problems

Problem 1 :

If p  =  sin θ + cos θ, q  =  sin θ - cos θ, then find the value of (p2 + q2).

Problem 2 :

If x  =  sec θ + tan θ, q  =   secθ + tan θ, then find the value of xy.

Problem 3 :

If a  =  csc θ + cot θ, b  =  csc θ - cot θ, then find the value of (a2 - b2).

Problem 4 :

Prove that Problem 5 :

Prove that

(secA − cosecA) (1 + tanA + cotA) = tanAsecA − cotA cosecA

Problem 6 :

Eliminate θ from

a cos θ  =  b

c sin θ  =  d

where a, b, c, d are constants. ## Basic Trigonometric Identities Worksheet - Solutions

Problem 1 :

If p  =  sin θ + cos θ, q  =  sin θ - cos θ, then find the value of (p2 + q2).

Solution :

p2 + q=  (sin θ + cos θ)2 + (sin θ - cos θ)2

p2 + q2  =  (sin2θ + cos2θ + 2sinθcosθ)

+ (sin2θ + cos2θ - 2sinθcosθ)

p2 + q2  =  2sin2θ + 2cos2θ

p2 + q2  =  2(sin2θ + cos2θ)

p2 + q2  =  2(1)

p2 + q2  =  2

Problem 2 :

If x  =  sec θ + tan θ, y  =  secθ + tan θ, then find the value of xy.

Solution :

xy  =  (sec θ + tan θ)(sec θ - tan θ)

xy  =  sec2θ - tan2θ

xy  =  1

Problem 3 :

If a  =  csc θ + cot θ, b  =  csc θ - cot θ, then find the value of (a2 - b2).

Solution :

a2 - b2  =  (csc θ + cot θ)2 - (csc θ - cot θ)2

a2 + b2  =  (csc2θ + cot2θ + 2cscθcotθ)

- (csc2θ + cot2θ - 2cscθcotθ)

a2 + b2  =  csc2θ + cot2θ + 2cscθcotθ

- csc2θ - cot2θ + 2cscθcotθ

a2 - b2  =  4cscθcotθ

Problem 4 :

Prove that Solution : Problem 5 :

Prove that

(secA − cosecA) (1 + tanA + cotA) = tanAsecA − cotA cosecA

Solution : From (i) and (ii), we get the required result.

Problem 6 :

Eliminate θ from

a cos θ  =  b

c sin θ  =  d

where a, b, c, d are constants.

Solution :

a cos θ  =  b

Multiply each side by c.

ac cos θ  =  bc

Square each side.

(ac cos θ)2  =  (bc)2

a2c2 cos2θ  =  b2c2 -----(1)

c sin θ  =  d

Multiply each side by a.

Square each side.

a2c2 sin2θ  =  a2d-----(2)

a2c2 cos2θ + a2c2 sin2θ  =  b2c+  a2d2

a2c2(cos2θ + sin2θ)  =  b2c2  +  a2d2

a2c2(1)  =  b2c2  +  a2d2

a2c2  =  b2c2  +  a2d2 After having gone through the stuff given above, we hope that the students would have understood the basic trigonometric identities.

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