Advertisements
Advertisements
Question
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
Solution
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = `(1 - (1)^2)/(1 + (1)^2)` ......[∵ tan 45° = 1]
= `(1 - 1)/(1 + 1)`
= `0/2`
= 0
RELATED QUESTIONS
Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
Prove the following trigonometric identities.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Prove the following identities:
`1 - sin^2A/(1 + cosA) = cosA`
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
If sinθ = `11/61`, find the values of cosθ using trigonometric identity.
Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\]
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
Prove that `(sec θ - 1)/(sec θ + 1) = ((sin θ)/(1 + cos θ ))^2`
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
If tan θ = `9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ......[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.