Advertisements
Advertisements
प्रश्न
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
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
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
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:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
cosec4θ − cosec2θ = cot4θ + cot2θ
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
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)`
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Evaluate:
sin2 34° + sin2 56° + 2 tan 18° tan 72° – cot2 30°
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.
Prove that: 2(sin6θ + cos6θ) - 3 ( sin4θ + cos4θ) + 1 = 0.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
Prove the following trigonometry identity:
(sinθ + cosθ)(cosecθ – secθ) = cosecθ.secθ – 2 tanθ