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प्रश्न
sec θ when expressed in term of cot θ, is equal to ______.
पर्याय
`(1 + cot^2 θ)/cotθ`
`sqrt(1 + cot^2 θ)`
`sqrt(1 + cot^2 θ)/cotθ`
`sqrt(1 - cot^2 θ)/cotθ`
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उत्तर
sec θ when expressed in term of cot θ, is equal to `underlinebb(sqrt(1 + cot^2 θ)/cotθ)`.
Explanation:
As we know that,
sec2 θ = 1 + tan2 θ
and cot θ = `1/tanθ`
`\implies` tan θ = `1/cotθ`
∴ sec2 θ = `1 + (1/cotθ)^2`
= `1 + 1/(cot^2 θ)`
`\implies` sec2 θ = `(cot^2 θ + 1)/(cot^2 θ)`
`\implies` sec θ = `sqrt(1 + cot^2 θ)/cotθ`
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संबंधित प्रश्न
Prove the following trigonometric identity.
`cos^2 A + 1/(1 + cot^2 A) = 1`
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
if `a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = n`Prove that `(m + n)^(2/3) + (m - n)^(2/3)`
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
If `sin theta = x , " write the value of cot "theta .`
Prove that:
`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
