Advertisements
Advertisements
प्रश्न
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
Advertisements
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
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
Prove the following trigonometric identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove the following trigonometric identities.
`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
`cosec theta (1+costheta)(cosectheta - cot theta )=1`
The value of sin2 29° + sin2 61° is
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.
