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प्रश्न
tan θ cosec2 θ – tan θ is equal to
पर्याय
sec θ
cot2 θ
sin θ
cot θ
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उत्तर
cot θ
Explanation;
Hint:
tan θ cosec2 θ – tan θ = tan θ (cosec2 θ – 1)
= `tan theta xx cot^2 theta`
= `1/cot theta xx cot^2 theta`
= cot θ
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संबंधित प्रश्न
Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that `(cot A)/(1 - tan A) + (tan A)/(1 - cot A) = 1 + tan A + cot A = sec A . "cosec" A + 1`.
