Question

if A and B are complementary angles , then prove that, sinA = √(cosA/sinA) - cosA×sinB​

Answer 1

I assume the last term to be cot^2(B)

Given: A = 90 - B => A+B = 90

=> Sin(A) = Cos(B), tan(A) = Cot (B) , sec^2 (A) = cosec^2 (B)

=>(sinA cosB + cosA sinB) - (tanA tanB) + sec^2(A) - cot^2(B)

= sin(A+B) - (cotB * tanB)+ (cosec^2 B - cot^2 B)

= sin(90) - 1 + 1

= 1