Q13 of 118 Page 5

If cot (α + β) = 0, then write the value of sin (α + 2β).

Given: cot(α + β) = 0

∴

⇒ cotα.cotβ = 1

Now,

Sin(α +2β ) = sinα.cos2β + cosα.sin2β

=sin α (2 cos² β-1)+cos α.2 sin β.cos β

Write the value of 2 (sin⁶ x + cos⁶ x) − 3 (sin⁴ x + cos⁴ x) + 1.

Write the value of cos 1° + cos 2° + cos 3° + ... + cos 180°.

If tan A + cot A = 4, then write the value of tan⁴ A + cot⁴ A.

Write the least value of cos² x + sec² x.