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प्रश्न
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
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उत्तर
sin θ = `11/61` ...[Given]
We have,
sin2θ + cos2θ = 1
⇒ cos2θ = 1 − sin2θ
⇒ cos2θ = `1 - (11/61)^2`
⇒ cos2θ = `1 - 121/3721`
⇒ cos2θ = `(3721 - 121)/3721`
⇒ cos2θ = `3600/3721`
⇒ cos θ = `sqrt((60/61)^2)` ...[Taking the square root of both sides]
⇒ cos θ = `60/61`
Thus, the value of cos θ is `60/61`.
संबंधित प्रश्न
Evaluate sin25° cos65° + cos25° sin65°
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`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - x^2/c^2 = 1`
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
` tan^2 theta - 1/( cos^2 theta )=-1`
Prove the following identities:
`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta )/(cos theta)`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
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 that `1/("cosec" θ - cot θ) = "cosec" θ + cot θ`.
If tan θ – sin2θ = cos2θ, then show that `sin^2θ = 1/2`.
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
If cot θ = `40/9`, find the values of cosec θ and sinθ,
We have, 1 + cot2θ = cosec2θ
1 + `square` = cosec2θ
1 + `square` = cosec2θ
`(square + square)/square` = cosec2θ
`square/square` = cosec2θ ......[Taking root on the both side]
cosec θ = `41/9`
and sin θ = `1/("cosec" θ)`
sin θ = `1/square`
∴ sin θ = `9/41`
The value is cosec θ = `41/9`, and sin θ = `9/41`
Eliminate θ if x = r cosθ and y = r sinθ.
