Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Advertisements
उत्तर
LHS = `(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA)`
= `((sinA + cosA)^2 + (sinA - cosA)^2)/((sinA + cosA)(sinA - cosA))`
= `(sin^2A + cos^2A + 2sinA cosA + sin^2A + cos^2A - 2sinA cosA)/(sin^2A - cos^2A)`
= `(2(sin^2A + cos^2A))/(sin^2A - cos^2A)`
= `2/(sin^2A - cos^2A)` [`sin^2A + cos^2A = 1`]
= `2/(sin^2A - cos^2A) = 2/(sin^2A - (1 - sin^2A))`
⇒ `2/(2sin^2A - 1)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
Prove the following identities:
`1/(secA + tanA) = secA - tanA`
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
