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प्रश्न
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
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उत्तर
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
⇒ `(sin(90^circ - 41^circ)/sin41^circ)^2 + (cos(90^circ - 49^circ)/sin49^circ)^2`
⇒ `(cos41^circ/sin41^circ)^2 + (sin49^circ/sin49^circ)^2`
⇒ 1 + 1 = 2
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संबंधित प्रश्न
Prove the following identities:
`(1 + sin A)/(1 - sin A) = (cosec A + 1)/(cosec A - 1)`
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Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
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∴ L.H.S. = R.H.S.
