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प्रश्न
Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.
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उत्तर
LHS = sin( 90° - θ ) sin θ cot θ
= cos θ . sin θ . `cos θ/sin θ`
= cos2θ
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
If sec θ = `25/7`, then find the value of tan θ.
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3.
