Question

someone solve this trigonometry question
prove the above it being given that a and b are complementary angles​

Answer 1

Answer:

Given: A and B are complementary angles

(sin A +cosB)2=1+2sinAsinB

To Find : A & B

Solution:

A and B are complementary angles

=> A + B = 90°

=> A = 90° -B

=> SinA = Sin(90° - B)

=> SinA = CosB

A = 90° - B

=> COSA = Cos(90° - B)

SinA = COSA

=> SinA = SinB

=> A = B

Hence True iff A = B

and A + B = 90°

=> A = B = 45°

if A & B are complementary then below can be proved:

(sinA +cosA)2=1+2 sinAsinB or (sin A +SinB)2=1+2 sinAsinB

(sinA +COSA)2=1+2 sinAsinB

LHS = 1+ 2SinACosA = 1 + 2SinASinB = RHS

(sinA +SinB)?=1+2sinAsinB

LHS = Sin?A + Sinb +2SinASinB = Sin?A +

Cos A + 2SinASinB = 1 + 2sinAsinB = RHS

=> CosA = SinB

(sin A +cosB)2=1+2sinAsinB

=> (sinA +sinA)?=1+2sinACosA

=> (2SinA)? = ( Sina + Cosa + 2sinACosA)

=> (2SinA)2 = ( SinA + CosA)?

=> 2 SinA = SinA + CosA

=> SinA = CosA

sorry pata nahi yeh correct h ya nahi .