Advertisements
Advertisements
Question
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
Options
True
False
Advertisements
Solution
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
RELATED QUESTIONS
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
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 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.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`
If `sec theta + tan theta = x," find the value of " sec theta`
What is the value of (1 + cot2 θ) sin2 θ?
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2 = 1`
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
