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प्रश्न
Prove the following identity :
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
उत्तर
LHS = `1/(sinA + cosA) + 1/(sinA - cosA)`
= `(sinA - cosA + sinA + cosA)/(sin^2A - cos^2A)`
= `(2sinA)/(1 - cos^2A - cos^2A) = (2sinA)/(1 - 2cos^2A)`
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Prove the following identity :
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Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
If sec θ = `25/7`, find the value of tan θ.
Solution:
1 + tan2 θ = sec2 θ
∴ 1 + tan2 θ = `(25/7)^square`
∴ tan2 θ = `625/49 - square`
= `(625 - 49)/49`
= `square/49`
∴ tan θ = `square/7` ........(by taking square roots)
