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
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities.
tan2 θ − sin2 θ = tan2 θ sin2 θ
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
If `(x/a sin a - 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`
If 5x = sec θ and \[\frac{5}{x} = \tan \theta\]find the value of \[5\left( x^2 - \frac{1}{x^2} \right)\]
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
If x = h + a cos θ, y = k + b sin θ.
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
If tan α + cot α = 2, then tan20α + cot20α = ______.
If cosA + cos2A = 1, then sin2A + sin4A = 1.
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`
If tan θ = `x/y`, then cos θ is equal to ______.
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
