Advertisements
Advertisements
प्रश्न
Prove the following that:
`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ
Advertisements
उत्तर
LHS: `((sin^3θ)/(cos^3θ))/((1 + sin^2θ)/(cos^2θ)) + ((cos^3θ)/(sin^3θ))/((1 + cos^2θ)/(sin^2θ))`
= `((sin^3θ)/(cos^3θ))/(((cos^2θ + sin^2θ))/cos^2θ) + ((cos^3θ)/(sin^3θ))/(((sin^2θ + cos^2θ))/sin^2θ)`
= `sin^3θ/cosθ + cos^3θ/sinθ`
= `(sin^4θ + cos^4θ)/(cosθsinθ)`
= `((sin^2θ + cos^2θ)^2 - 2 sin^2θ cos^2θ)/(cosθ sinθ)`
= `(1 - 2 sin^2θ cos^2θ)/(cosθ sinθ)`
= `1/(cos θ sinθ) - (2 sin^2θcos^2θ)/(cosθ sinθ)`
= secθ cosec θ – 2 sinθ cosθ
= RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Find the value of `(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)`
What is the value of (1 + cot2 θ) sin2 θ?
\[\frac{x^2 - 1}{2x}\] is equal to
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
Choose the correct alternative:
1 + cot2θ = ?
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
