If A+B=90 then the simplest form of 
is ?
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Answered by
3
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
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sinB
#answerwithquality #bal
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