Advertisements
Advertisements
प्रश्न
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
Advertisements
उत्तर
We have ,
`sqrt(3) sin theta = cos theta`
⇒ `sin theta/ cos theta = 1/ sqrt(3)`
⇒ `tan theta = 1/ sqrt(3)`
⇒ `tan theta = tan 30°`
∴ `theta = 30°`
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
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.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
cos4 A − sin4 A is equal to ______.
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
Prove that sin4θ - cos4θ = sin2θ - cos2θ
= 2sin2θ - 1
= 1 - 2 cos2θ
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
Prove the following identity:
(sin2θ – 1)(tan2θ + 1) + 1 = 0
Prove the following trigonometry identity:
(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ
