Advertisements
Advertisements
प्रश्न
If `cos θ = 24/25`, then sin θ = ?
Advertisements
उत्तर
`cos θ = 24/25` ...[Given]
We know that,
sin2θ + cos2θ = 1
∴ `sin^2θ + (24/25)^2 = 1`
∴ `sin^2θ + 576/625 = 1`
∴ `sin^2θ = 1 - 576/625`
∴ `sin^2θ = (625 - 576)/625`
∴ `sin^2θ = 49/625`
∴ `sin θ = 7/25` ...[Taking square root of both sides]
APPEARS IN
संबंधित प्रश्न
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
Prove the following trigonometric identities.
`(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`
If `a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = n`, prove that `(m + n)^(2/3) + (m - n)^(2/3) = 2a^(2/3)`
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Prove the following identity :
`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Find A if tan 2A = cot (A-24°).
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
Prove that sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A.
