Advertisements
Advertisements
प्रश्न
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
विकल्प
`1/sqrt(3)`
`sqrt(3)`
1
0
Advertisements
उत्तर
If cos 9α = sinα and 9α < 90°, then the value of tan5α is 1.
Explanation:
According to the question,
cos 9α = sin α and 9α < 90°
i.e. 9α is an acute angle
We know that,
sin(90° – θ) = cos θ
So, cos 9α = sin(90° – α)
Since, cos 9α = sin(90° – 9α) and sin(90° – α) = sin α
Thus, sin(90° – 9α) = sin α
90° – 9α = α
10α = 90°
α = 9°
Substituting α = 9° in tan 5α, we get,
tan 5α = tan(5 × 9°)
= tan 45°
= 1
∴ tan 5α = 1
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
If \[\cos A = \frac{7}{25}\] find the value of tan A + cot A.
Prove the following identity :
`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
Prove that `(sin^2theta)/(cos theta) + cos theta` = sec θ
