Advertisements
Advertisements
Question
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
Advertisements
Solution
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
RELATED QUESTIONS
If (secA + tanA)(secB + tanB)(secC + tanC) = (secA – tanA)(secB – tanB)(secC – tanC) prove that each of the side is equal to ±1. We have,
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
Simplify : 2 sin30 + 3 tan45.
What is the value of (1 − cos2 θ) cosec2 θ?
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
Prove that `(cos(90 - "A"))/(sin "A") = (sin(90 - "A"))/(cos "A")`
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
Prove the following:
`1 + (cot^2 alpha)/(1 + "cosec" alpha)` = cosec α
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
