Question

Prove that

(i) sin 75° = (√6 + √2)/4

(ii) cos135° - cos120°/cos135° + cos120° = (3 - 2√2)

(iii) tan 15° + cot 15° = 4

Answer 1

(i) sin75° = sin(90° - 15°) .…….(using sin(A - B) = sinAcosB - cosAsinB)

= sin90°cos15° - cos90°sin15°

= 1.cos15° - 0.sin15°

= cos15°

Cos15° = cos(45° - 30°) …………(using cos(A - B) 

= cosAcosB + sinAsinB)

= cos45°.cos30° + sin45°.sin30°

(iii) tan15° + cot15° =

First, we will calculate tan15°,

Putting in eq(1),