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प्रश्न
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
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उत्तर
`tan35^circ cot(90^circ - θ) = 1`
Given `tan35^circ cot(90^circ - θ) = 1`
⇒ `tan35^circtanθ = 1`
⇒ `tan35^circ = cotθ`
⇒ `tan35^circ = tan(90^circ - θ)`
⇒ `90^circ - θ = 35^circ`
⇒ `θ = 55^circ`
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संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 - sin θ)/(1 + sin θ) = (sec θ - tan θ)^2`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
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)
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
