Question

Is secant theta + tan theta equal to p show that p square - 1 / p square + 1 equal to sin theta?

Answer 1

Answer:

Step-by-step explanation:

R.H.S:

(p²-1) / (p²+1)

= [(secθ+tanθ)2-1] / [(secθ+tanθ)2+1]

= (sec²θ+tan²θ+2secθtanθ-1) / (sec²θ+tan²θ+2secθtanθ+1)

= (Sec²θ-1)+tan²θ+2secθtanθ / (1+tan²θ)+sec²θ+2secθtanθ

= tan²θ+tan²θ+2secθtanθ / sec²θ+sec²θ+2secθtanθ [sec²θ - 1=tan²θ]

= 2tan²θ+2secθtanθ / 2sec²θ+2secθtanθ

= 2tanθ(tanθ+secθ) / 2secθ(secθ+tanθ)

= tanθ / secθ

= sinθ/cosθ / 1/cosθ [tanθ=sinθ/cosθ and secθ=1/cosθ ]

= sinθ/1

= sinθ

= L.H.S

Hence Proved.