TRIGONOMETRY PROBLEMS WORKSHEET

(1)  Find the value of cos 2A, A lies in the first quadrant, when

(i) cos A = 15/17

(ii) sin A = 4/5

(iii) tan A = 16/63           Solution

(2)  f θ is an acute angle, then find

(i) sin (π/4 - θ/2), when sin θ = 1/25          Solution

(ii) cos (π/4 + θ/2), when sin θ = 8/9          Solution

(3)  If cos θ  =  (1/2) (a + 1/a), show that cos 3θ  =  (1/2) (a³ + 1/a³)        Solution

(4)  Prove that cos 5θ = 16cos⁵ θ − 20 cos³ θ + 5cos θ

Solution

(5)  Prove that sin 4α = 4 tan α [(1 − tan²α)/(1 + tan²α)²]

Solution

(6)  If A + B = 45^◦, show that (1 + tan A) (1 + tan B) = 2.

Solution

(7)  Prove that (1 + tan 1^◦)(1 + tan 2^◦)(1 + tan 3^◦) ................(1 + tan 44^◦) is a multiple of 4.         Solution

(8)  Prove that tan (π/4 + θ) - tan (π/4 − θ)  =  2 tan 2θ.

Solution

(9)  Show that cot (7  ½^◦) =   √2 + √3 + √4 + √6

Solution

(10)  Prove that

(1 + sec2θ)(1 + sec4θ).............(1 + sec2ⁿθ)  =  tan2ⁿθcotθ 

Solution

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