Advertisements
Advertisements
प्रश्न
` tan^2 theta - 1/( cos^2 theta )=-1`
Advertisements
उत्तर
LHS= `tan^2 theta - 1/(cos^2 theta)`
=` (sin^2 theta )/( cos^2 theta) - 1/(cos^2 theta)`
=`(sin ^2 theta-1)/(cos^2 theta)`
=` (-cos^2 theta )/(cos^2 theta)`
= -1
= RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following trigonometric identities.
`tan A/(1 + tan^2 A)^2 + cot A/((1 + cot^2 A)) = sin A cos A`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Without using trigonometric table , evaluate :
`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
Given that sin θ = `a/b`, then cos θ is equal to ______.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
