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प्रश्न
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
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उत्तर
Given:` secθ+tanθ=x`
We know that,
`Sec^2θ-tan^2θ=1`
Therefore,
`sec^2 θ-tan^2θ=1`
⇒` (Secθ+tan θ) (Secθ-tan θ)=1`
⇒` x (secθ-tan θ )=1`
⇒ `(sec θ-tan θ)=1/x`
Hence, `sec θ-tan θ=1/4`
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संबंधित प्रश्न
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
Prove the following identities:
`(secA - tanA)/(secA + tanA) = 1 - 2secAtanA + 2tan^2A`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
Prove that `( sintheta - 2 sin ^3 theta ) = ( 2 cos ^3 theta - cos theta) tan theta`
If `(cosec theta - sin theta )= a^3 and (sec theta - cos theta ) = b^3 , " prove that " a^2 b^2 ( a^2+ b^2 ) =1`
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
Define an identity.
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2 "cosec"θ`
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = "cosec" θ - cot θ`.
Prove that cosec θ – cot θ = `sin theta/(1 + cos theta)`
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
