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प्रश्न
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
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उत्तर
L.H.S. = cosec4 A – cosec2 A
= cosec2 A (cosec2 A – 1)
R.H.S. = cot4 A + cot2 A
= cot2 A (cot2 A + 1)
= (cosec2 A – 1) cosec2 A
Thus, L.H.S. = R.H.S.
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संबंधित प्रश्न
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Show that : tan 10° tan 15° tan 75° tan 80° = 1
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S. = `square`
= `square/(sinθ) + (sinθ)/(cosθ)`
= `(cos^2θ + sin^2θ)/square`
= `1/(sinθ.cosθ)` ...`[cos^2θ + sin^2θ = square]`
= `1/(sinθ) xx 1/square`
= `square`
= R.H.S.
