[(1-sin alpha)(1+sin alpha)],[cos(A-B)=cos A*cos B+sin A*sin B afe A=B=60^(@)]

If sin A=(1)/(sqrt(5)) and sin B=(1)/(sqrt(10)) ,find the values of cos A and cos B .Hence using the formula cos(A+B)=cos A cos B-sin A sin B, show that (A+B)=45^(@).

If A = [(cos alpha, sin alpha),(sin alpha, cos alpha)] and B = [(cos beta, sin beta),(sin beta, cos beta)] show that AB = BA

Prove that formula cos(A-B)=cos A*cos B+sin A*sin Bwith the help of the formula sin(A+B)=sin A*cos B+cos A*sin B

If (cos alpha,sin alpha),B(sin alpha,-cos alpha),C(1,2)A(cos alpha,sin alpha),B(sin alpha,-cos alpha),C(1,2) are the vertices of $ABC, then as alpha varies, find the locus of its centroid.

If cos (A+B) = alpha cos A cos B + beta sin A sin B, then (alpha, beta) is

If pi

If A = 60 ^(@) and B = 30 ^(@) , find the value of (sin A cos B+ cos A sin B)^(2) + (cos A cos B - sin A sin B )^(2)

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is

If A=[(cos^(2)alpha, cos alpha sin alpha),(cos alpha sin alpha, sin^(2)alpha)] and B=[(cos^(2)betas,cos beta sin beta),(cos beta sin beta, sin^(2) beta)] are two matrices such that the product AB is null matrix, then alpha-beta is