Question

26. Prove that
(Sin Q + Cos Q)/ (Sin Q – Cos Q) + (Sin Q – Cos Q) / (Sin Q + Cos Q) = 2 / (2 Sin2Q – 1).

Answer 1

Answer:

L.H.S

ITS VERY EASY

==> (SIN Q + COS Q) / (SINQ - COSQ) + (SINQ-COSQ) / (SINQ+COSQ)

==> BY LCM

==> (SINQ+COSQ)² + (SINQ-COSQ)² ÷ (SINQ-COSQ)(SINQ+COSQ)

==> SIN²Q + COS²Q + 2SINQCOSQ +  SIN²Q + COS²Q - 2SINQCOSQ ÷ (SIN²Q - COS²Q)

==> 1 + 2 SINQCOSQ + 1 - 2SINQCOSQ ÷ (SIN²Q - COS²Q)

==> 1 + 1 ÷ SIN²Q - (1-SIN²Q)

==> 2 ÷ SIN²Q - 1 + SIN²Q

==> 2 ÷ 2SIN²Q - 1

==> 2/ 2SIN²Q - 1 = R.H.S

I HOPE ITS HELPFUL