Advertisements
Advertisements
प्रश्न
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
Advertisements
उत्तर
Given:
`sin θ=1/3`
⇒ `1/ sinθ=3`
⇒` cosec θ=3`
We know that,
`cosec^2θ-cot ^2θ=1`
⇒`(3)^2-cot^2θ=1`
⇒ `cot ^2 θ=9-1`
Therefore,
`2 cot ^2 θ+2=2xx8+2`
=`16+2`
= `18`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove the following trigonometric identities
`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove the following trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following identities:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
If `(x/a sin a - y/b cos theta) = 1 and (x/a cos theta + y/b sin theta ) =1, " prove that "(x^2/a^2 + y^2/b^2 ) =2`
If `( tan theta + sin theta ) = m and ( tan theta - sin theta ) = n " prove that "(m^2-n^2)^2 = 16 mn .`
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
Prove that `(sec A)/(tan A + cot A) = sin A`.
Prove that sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A.
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
