Question

A and B are complementary angles.then the value of(sinA cosB +cos AsinB- tanA+tanB + sec²A - cot²B) is

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

Answer 2

Answer:

1

Step-by-step explanation:

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