1.

Sina/1-tan+cosa/1-cota=Sina+cosa​

Answer»

ANSWER:

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

What is the smartest way for transferring heavy DATA?

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.


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