Question

sinA(1+tanA) + cosA(1+cotA) =​

Answer 1

Answer:

How do you prove that sinA(1+tanA)+cosA(1+cotA)=secA+cosecA?

To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.

LHS = sin A(1+ tan A)+ cos A(1 + cot A)

= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A

= sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A

=[ sin^2 A cos A + cos^2 A sin A + sin^3 A + cos^3 A]/sin A cos A

= [ sin^2 A cos A +cos^3 A + cos^2 A sin A + sin^3 A]/sin A cos A

= [cos A (sin^2 A + cos^2 A) + sin A (sin^2 A + cos^2 A)]/sin A cos A

= [cos A +sin A]/sin A cos A

= (1/sin A) + (1/cos A)

= cosec A + sec A = RHS.

Proved.

Answer 2

Answer:

SecA +Cosec A

Step-by-step explanation:

Sin A + Sin^2A/Cos A + Cos A + Cos^2A/Sin a

= sin+ 1/Cos - cos + cos +1/sin-sin

= 1/Cos + 1/sin

= sec+ cosec