Question

Double and half angle identities?

Answer 1

Double and half angle identities are trigonometric identities used to simplify trigonometric expressions and solve trigonometric equations.

Step-by-step explanation:

Double and half angle identities are trigonometric identities that involve angles that are double or half the given angle. These identities are useful in simplifying trigonometric expressions and solving trigonometric equations.

For example, the double angle identity for the sine function is sin(2θ) = 2sin(θ)cos(θ). This identity allows us to express the sine of a double angle in terms of the sine and cosine of the original angle.

Similarly, the half angle identity for the cosine function is cos(θ/2) = ±√((1 + cos(θ))/2). This identity allows us to express the cosine of a half angle in terms of the cosine of the original angle.

Answer 2

Option 4

Step-by-step explanation:

Given:

Sinθ =
`(15)/(17)`

Since, cos2θ = 1 - 2sin²θ

cos2θ =
`1-2((15)/(17))^2`

cos2θ = 1 -
`(450)/(289)`

cos2θ =
`(289-450)/(289)`

cos2θ =
`-(161)/(289)`

Therefore, Option 4 will be the answer.