Advertisements
Advertisements
प्रश्न
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
Advertisements
उत्तर
If `sqrt(3)` sin θ – cos θ = θ
To prove tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
`sqrt(3)` sin θ – cos θ = θ
`sqrt(3)` sin θ = cos θ
`sin theta/cos theta = 1/sqrt(3)`
tan θ = tan 30°
θ = 30°
L.H.S = tan 3θ°
= tan3 (30°)
= tan 90°
= undefined (α)
R.H.S = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
= `(3tan30^circ - tan^2 30^circ)/(1 - 3tan^2 30^circ)`
= `3(1/sqrt(3)) - (1/sqrt(3))^3 ÷ 1 - 3 xx (1/sqrt(3))^2`
= `sqrt(3) - 1/(3sqrt(3)) ÷ 1 - 3 xx 1/3`
= `(9 - 1)/(3sqrt(3)) ÷ 1 - 1`
= `8/(3sqrt(3)) ÷ 0`
= undefined (α)
∴ tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
What is the value of \[6 \tan^2 \theta - \frac{6}{\cos^2 \theta}\]
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
