Trigonometry Problems Worksheet :
Here we are going to see some practice questions in trigonometry. For each problem you can find step by step solution.
(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
(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.
(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.
(9) Show that cot (7 ½◦) = √2 + √3 + √4 + √6
(10) Prove that (1 + sec 2θ)(1 + sec 4θ).............(1 + sec 2nθ) = tan 2n θ cot θ
After having gone through the stuff given above, we hope that the students would have understood how to solve higher grade trigonometry problems.
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