Question

If sin A=CsB,then prove that A+B=90°

50 points...have a nice day Friends

Answer 1

Hello Friend....

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The answer of u r question is......

Ans:

Given,

SinA=cosB

we know cosB=Sin(90°-B)......(1)

SinA=sin(90°B)

If A,B are acute angles then,A=90°-B

so,

A+B=90°

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Thank you.....⭐️⭐️⭐️⭐️

Answer 2

$\boxed{ \mathfrak{Hey \: there}}$

Given :- SinA = CosB

Required to prove :- A + B = 90°

$\bf \: Proof$

→ SinA = CosB

⭐ lets have Sin on both sides

→ SinA = Cos (90-B )

$\boxed{cos \: (90-ø) \: = Sinø}$

→ SinA = SinB

⭐ Sin on LHS and RHS get cancelled

→ A = B

So let's take a constant

→ A = B = K

A + B = 90°

→ K + K = 90°

→ 2K = 90°

→ K = 90/2

→ k = 45°

A = B = 45°

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$\bf \: Verification$

→ A + B = 90°

→ 45° + 45° = 90°

→ 90° = 90°

$\bf \: Hence \: proved$

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$\boxed{ \mathfrak{Hope \: it \: Helps \: u}}$