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 trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
Write the value of tan10° tan 20° tan 70° tan 80° .
If `sec theta = x ,"write the value of tan" theta`.
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
If cosθ = `5/13`, then find sinθ.
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
If 2sin2β − cos2β = 2, then β is ______.
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
