`(sin theta + cos theta)^2 = 1 + 2 sin theta cos theta`

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

((1 + sin theta-cos theta) / (1 + sin theta + cos theta)) ^ (2) = (1-cos theta) / (1 + cos theta)

Prove each of the following identities : (sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = (2) /((sin^(2) theta - cos^(2) theta)) = (2) /((2sin^(2) theta -1))

((sin theta+cos theta)^(2)-1)/(sin theta*cos theta)

(sin theta-cos theta)^(2)*(sin theta+cos theta)^(2)=

Prove each of the following identities : (i) (1+ cos theta + sin theta)/(1+ cos theta - sin theta) =(1+ sin theta)/(cos theta) (ii) (sin theta + 1- cos theta)/(cos theta - 1 + sin theta) = (1+ sin theta)/(cos theta)

If 5 cos theta -12 sin theta =0 , the value of (2 sin theta +cos theta )/(cos theta - sin theta ) यदि 5 cos theta -12 sin theta =0 , है, तो (2 sin theta +cos theta )/(cos theta - sin theta ) का मान ज्ञात करें |

2 cos (theta - pi //2) + 3 sin (theta + pi//2) - (3sin theta + 2 cos theta ) = ? A. cos theta - sin theta B. sin theta - cos theta C. sin theta + cos theta D. cot theta - tan theta .

(sin theta+cos theta)(1-sin theta cos theta)=sin^3 theta+cos^3 theta

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] "then " f (pi/7) is