Math, asked by hardikaajara, 9 months ago

If A+B=90 then the simplest form of $\sqrt{sinA secB - sinA cosB}$ is ?

Answers

Answered by rishu6845

Answer:

SinB

Step-by-step explanation:

Given---> A + B = 90°

To find---> √{ SinA SecB - SinA CosB )

Solution---> ATQ, A + B = 90°

Now,

SinA SecB - SinA CosB

= SinA ( SecB - CosB )

= SinA { ( 1 / CosB ) - CosB }

= SinA { ( 1 - Cos²B ) / CosB }

Putting A = 90° - B , and using Sin²θ = 1 - Cos²θ , we get,

= Sin( 90° - B ) × Sin²B / CosB

we know that Sin ( 90° - θ ) = Cosθ , we get,

= CosB × Sin²B / CosB

CosB is cancel out from numerator and denominator and we get

= Sin²B

Now returning to original problem

√{SinA SecB - SinA CosB ) = √Sin²B

= SinB

Answered by Aɾꜱɦ

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sinB

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