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प्रश्न
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
पर्याय
cos θ
sin θ
tan θ
cot θ
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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
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संबंधित प्रश्न
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
If `sec theta = x ,"write the value of tan" theta`.
Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Choose the correct alternative:
cot θ . tan θ = ?
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
