Question

Q(psquare-1)=2p,where sintheta+costheta=p and sectheta+cosec theta=q

Answer 1

q (p² - 1) = 2p

Step-by-step explanation:

L.H.S. = q (p² - 1)

= (secθ + cosecθ) {(sinθ + cosθ)² - 1}

= (secθ + cosecθ) (sin²θ + cos²θ + 2 sinθ cosθ - 1)

= (secθ + cosecθ) (1 + 2 sinθ cosθ - 1)

= 2 sinθ cosθ (secθ + cosecθ)

= 2 sinθ cosθ (1/cosθ + 1/sinθ)

= 2 sinθ cosθ * (sinθ + cosθ)/(sinθ cosθ)

= 2 (sinθ + cosθ)

= 2p = R.H.S.

Hence proved.

Trigonometry:

Trigonometry is the study of relations between angles and their ratios with various properties to find sine, cosine, tan, cosec, sec and cot ratios. Some properties can deduce angles in their general value apart from known definite ones. Now let us know some identities-

1. sin²θ + cos²θ = 1

2. sec²θ - tan²θ = 1

3. cosec²θ - cot²θ = 1

Answer 2

Question :-

Q(P²-1)= 2P ,prove it

where , P = sin@ + cos@ and ,

Q = sec@ + cosec@

Proof :-

(Here assume @ as theta .)

Taking left hand side

→ Q(P² - 1 )

→ ( sec@ + cosec@ )( sin²@ + cos²@ +2sin@ cos @ - 1)

→ ( sec@ + cosec@) (2sin@ cos@)

→ 1/cos@ • 2sin@cos@ + 1/sin@•3sin@cos@

→ 2sin@ + 2cos@

→2 (sin@ + cos@)

•.• P = sin@ + cos@

→ 2P

Left hand side = Right hand side

hence proved .