Advertisements
Advertisements
प्रश्न
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
Advertisements
उत्तर
Given: sinθ = `11/61`
We know that,
sin2θ + cos2θ = 1
∴ `(11/61)^2 + cos^2θ` = 1
∴ `121/3721 + cos^2θ` = 1
∴ cos2θ = `1 - 121/3721`
∴ cos2θ = `(3721 - 121)/3721`
∴ cos2θ = `3600/3721`
∴ cosθ = `60/61` .......[Taking square root of both sides]
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove the following trigonometric identities
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
Prove the following trigonometric identities.
`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
If sec θ + tan θ = x, then sec θ =
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
sec θ when expressed in term of cot θ, is equal to ______.
(1 + sin A)(1 – sin A) is equal to ______.
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
