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प्रश्न
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
पर्याय
30°
45°
60°
90°
उत्तर
30°
sin θ = `1/2`
∴ θ = 30° ...[sin 30° = `1/2`]
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संबंधित प्रश्न
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
`(1+ cos theta)(1- costheta )(1+cos^2 theta)=1`
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
Write the value of `(cot^2 theta - 1/(sin^2 theta))`.
Write the value of cos1° cos 2°........cos180° .
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.
Activity:
L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
= `tan^2theta (1 - square)`
= `tan^2theta xx square` .....[1 – cos2θ = sin2θ]
= R.H.S
Prove that `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
sin(45° + θ) – cos(45° – θ) is equal to ______.
