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प्रश्न
If `cos θ = 24/25`, then sin θ = ?
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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]
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संबंधित प्रश्न
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove that `cosA/(1+sinA) + tan A = secA`
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
` tan^2 theta - 1/( cos^2 theta )=-1`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove that `(tan θ)/(cot(90° - θ)) + (sec (90° - θ) sin (90° - θ))/(cosθ. cosec θ) = 2`.
Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2 = 1`
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
If `sec θ + tan θ = sqrt(3)`, complete the activity to find the value of sec θ – tan θ.
Activity:
`square = 1 + tan^2θ` ...[Fundamental trigonometric identity]
`square - tan^2θ = 1`
`(sec θ + tan θ) . (sec θ - tan θ) = square`
`sqrt(3) . (sec θ - tan θ) = 1`
`(sec θ - tan θ) = square`
Prove that `(sin θ + tan θ)/(cos θ) = tan θ (1 + sec θ)`.
Prove that `(1 + sin θ)/(1 - sin θ) = (sec θ + tan θ)^2`.
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
If 2sin2θ – cos2θ = 2, then find the value of θ.
