Question

P.T cos (A+B) - 2cosA + cos (A-B)/ sin (A+B) - 2sinA + sin(A-B) = cotA.​

Answer 1

Answer:

Step-by-step explanation:

cos (A+B) - 2cosA + cos (A-B)/ sin (A+B) - 2sinA + sin(A-B)

Let us solve Numerator and denominator separately for clarity purpose.

Numerator:

Cos (A+B) - 2CosA + Cos (A-B)

= CosACosB - SinASinB - 2CosA+ CosACosb + SinASinB

= 2 CosACosB - 2 CosA

= 2CosA(CosB - 1) -----------------> [1]

Denominator:

Sin (A+B) - 2SinA + Sin(A-B)

=SinACosB+ CosASinB - 2 SinA + SinACosB - CosASinB

= 2SinACosB - 2SinA

= 2SinA(CosB - 1) ----------------------- [2]

Now substitute the values back in the numerator and denominator i.e. [1] / [2]

=> 2CosA(CosB - 1)  / 2SinA(CosB - 1)

=> CosA/SinA

= CotA.

= R.H.S

Hence proved.