Advertisements
Advertisements
प्रश्न
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
विकल्प
cos θ
sin θ
tan θ
cot θ
Advertisements
उत्तर
sin θ
Explanation:
`tan θ xx sqrt(1 - sin^2 θ) ...{sin^2 θ + cos^2 θ = 1, ∴ cos^2 θ = 1 - sin^2 θ}`
= `tan θ xx sqrt(cos^2 θ)`
= tan θ × cos θ
= `(sin θ)/(cos θ)` × cos θ
= sin θ
APPEARS IN
संबंधित प्रश्न
Prove that `\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }+\frac{\sin\theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{2}{2\sin^{2}\theta -1}`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(1+ secA)/sec A = (sin^2A)/(1-cosA)`
[Hint : Simplify LHS and RHS separately.]
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
