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प्रश्न
Prove the following identities:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
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उत्तर
L.H.S. = (sin A + cosec A)2 + (cos A + sec A)2
= sin2 A + cosec2 A + 2 sin A cosec A + cos2 A + sec2 A + 2 cos A sec A
= `sin^2A + cosec^2A + 2sinA xx 1/sinA + cos^2A + sec^2A + 2cosA xx 1/cosA`
= sin2 A + cos2 A + cosec2 A + sec2 A + 2 + 2 ...(∵ sin2 A + cos2 A = 1)
= 1 + cosec2 A + sec2 A + 4
= (1 + cot2 A) + (1 + tan2 A) + 5 ...[∵ cosec2 A = 1 + cot2 A and sec2 A = 1 + tan2 A]
= 1 + cot2 A + 1 + tan2 A + 5
= 7 + tan2 A + cot2 A
= R.H.S.
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संबंधित प्रश्न
Prove the following trigonometric identities.
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Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
Which is not correct formula?
`5/(sin^2θ) - 5cot^2θ`, complete the activity given below.
Activity:
`5/(sin^2θ) - 5cot^2θ`
= `square (1/(sin^2θ) - cot^2θ)`
= `5(square - cot^2θ) ...[1/(sin^2θ) = square]`
= 5(1)
= `square`
