Advertisements
Advertisements
प्रश्न
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
पर्याय
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
Let a = 2, then `a + 1/a = 2 + 1/2 = 5/2`
If 2sinθ = `a + 1/a`, then a
2sinθ = `5/2`
⇒ sinθ = `5/4` = 1.25
Which is not possible ...[∵ sin θ ≤ 1]
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove the following trigonometric identities:
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
Prove the following trigonometric identities.
If cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
Prove that cot2θ × sec2θ = cot2θ + 1.
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
