" ii) "sin(45^(@)-theta)=-(1)/(sqrt(2))(sin theta-cos theta)

tan(45^(@)+(1)/(2)theta)=sqrt((1+sin theta)/(1-sin theta))

Solve int((sin theta+sqrt(cos^(2)theta+2sin^(2)theta))^(n))/(sqrt(1+sin^(2)theta))cos theta d theta , where n ne -1 .

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

If (sin^(3)theta-cos^(3)theta)/(sin theta-cos theta)-(cos theta)/(sqrt(1+cot^(2)theta))-2 tan theta cot theta=-1 (AA theta in[0, 2pi], then

If (sin^(3)theta-cos^(3)theta)/(sin theta-cos theta)-(cos theta)/(sqrt(1+cot^(2)theta))-2 tan theta cot theta=-1 (AA theta in[0, 2pi], then

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

If sin theta+cos theta=sqrt(2) and b=(sqrt(2)(sin theta+cos theta))/(sin theta cos theta), then 'b'is equal to

Prove that sin (45^(@) + theta) - sin (45^(@) - theta) = sqrt(2) sin 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))

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)/12)=