Advertisements
Advertisements
प्रश्न
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
Advertisements
उत्तर
`tan^2 theta + sin theta = cos^2 theta`
LHS = `tan^2 theta + sin theta `
=`(sin^2 theta)/(cos^2 theta) + sin theta`
=` (1- cos^2 theta )/( cos^2 theta) + sin theta`
=` sec^2 theta -1 + sin theta `
Since LHS ≠ RHS, this is not an identity.
APPEARS IN
संबंधित प्रश्न
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following trigonometric identities.
`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`
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`
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?
9 sec2 A − 9 tan2 A is equal to
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
If cosθ = `5/13`, then find sinθ.
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
Prove that `(cos(90^circ - A))/(sin A) = (sin(90^circ - A))/(cos A)`.
Prove that `(cosθ)/(1 + sinθ) = (1 - sinθ)/(cosθ)`.
