Advertisements
Advertisements
प्रश्न
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Advertisements
उत्तर
`cos theta = 5/13`
`sin^2 theta = 1 - cos^2 theta = 1 - 25/169 = 144/169`
`sin theta = +- 12/13` as `theta` is acute, therefore `sintheta` must be positive
`:. sin theta = 12/13`
APPEARS IN
संबंधित प्रश्न
If `sec alpha=2/sqrt3` , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.
Prove that `cosA/(1+sinA) + tan A = secA`
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following trigonometric identities.
`(1 + sin θ)/cos θ+ cos θ/(1 + sin θ) = 2 sec θ`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
If `(x/a sin theta - y/b cos theta) = 1` and `(x/a cos theta + y/b sin theta) = 1`, prove that `(x^2/a^2 + y^2/b^2) = 2`.
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Write the value of cosec2 (90° − θ) − tan2 θ.
If \[\sin \theta = \frac{1}{3}\] then find the value of 9tan2 θ + 9.
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
sec2θ – tan2θ = ?
