# 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]

(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/+ θ) - tan (π/− 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

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