Advertisements
Advertisements
प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove that `(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Advertisements
उत्तर
L.H.S = `(sin theta-2sin^3theta)/(2cos^3theta -costheta)`
= `(sintheta(1-2sin^2theta))/(costheta(2cos^2theta-1))`
= `(sinthetaxx(1-2sin^2theta))/(costhetaxx{2(1-sin^2theta)-1})`
= `(sin thetaxx(1-2sin^2theta))/(costhetaxx(1-2sin^2theta))`
= `tantheta`
= R.H.S
APPEARS IN
संबंधित प्रश्न
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove the following identities:
`(i) 2 (sin^6 θ + cos^6 θ) –3(sin^4 θ + cos^4 θ) + 1 = 0`
`(ii) (sin^8 θ – cos^8 θ) = (sin^2 θ – cos^2 θ) (1 – 2sin^2 θ cos^2 θ)`
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following trigonometric identity.
`cos^2 A + 1/(1 + cot^2 A) = 1`
Prove the following trigonometric identities.
`(1 - sin theta)/(1 + sin theta) = (sec theta - tan theta)^2`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`(cos^3 theta +sin^3 theta)/(cos theta + sin theta) + (cos ^3 theta - sin^3 theta)/(cos theta - sin theta) = 2`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
If \[\cos A = \frac{7}{25}\] find the value of tan A + cot A.
9 sec2 A − 9 tan2 A is equal to
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
Prove that:
tan (55° + x) = cot (35° – x)
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove that
sec2A – cosec2A = `(2sin^2"A" - 1)/(sin^2"A"*cos^2"A")`
If cosec A – sin A = p and sec A – cos A = q, then prove that `("p"^2"q")^(2/3) + ("pq"^2)^(2/3)` = 1
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
If 5 tan β = 4, then `(5 sin β - 2 cos β)/(5 sin β + 2 cos β)` = ______.
