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प्रश्न
tan θ cosec2 θ – tan θ is equal to
विकल्प
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 the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Write True' or False' and justify your answer the following:
\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
Show that, cotθ + tanθ = cosecθ × secθ
Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
