Which of the following are identities sinalphacosalpha tan

Which of the following are identities? -sin(-alpha)/cos(-alpha) = tan alpha sec theta - sin theta * tan theta = cos theta (sin x + 1)^2 + cos^2 x = 2 sin theta + cos theta/cos theta = tan theta + 1 B, D A, B, D A, B, C All are identities

Solution

A. -sin(-alpha)/cos(-alpha) = tan alpha

Starting with left side

-sin(-alpha)/cos(-alpha)

And sin (-theta)=-sin theta , cos(-theta) = cos theta

-(-sin alpha)/cos alpha = sin alpha/cos alpha =tan alpha

Its an identity

b. sec theta - sin theta tan theta= cos theta

starting with left side

sec theta-sin theta tan theta

sec theta=1/cos theta         tan theta=sin theta/cos theta

1/cos theta - sin theta*sin theta/cos theta

1-sin²theta/cos theta = cos²theta/cos theta = cos theta

Its an identity

c. (sin x +1)² + cos²x=2

Starting with left side

(sinx + 1)²+cos²x

sin²x+1+2sinx+cos²x =    1+1 + 2sinx = 2 +2sinx

Its not an identity

d) (sin theta + cos theta)/cos theta = tan theta + 1

starting with left side

(sin theta + cos theta)/cos theta

sin theta/cos theta + cos theta/cos theta

tan theta + 1

Its an identity

Hence the correct option is

A,B,D