Advertisements
Advertisements
प्रश्न
`(sec^2 theta-1) cot ^2 theta=1`
Advertisements
उत्तर
LHS = `(sec^2 theta -1 ) cot^2 theta`
=`tan^2theta xx cot^2 theta (∵ sec^2 theta - tan^2 theta =1)`
=`1/(cot^2theta) xx cot^2 theta`
=1
=RHS
APPEARS IN
संबंधित प्रश्न
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
if `cosec theta - sin theta = a^3`, `sec theta - cos theta = b^3` prove that `a^2 b^2 (a^2 + b^2) = 1`
Prove the following identities:
`1 - sin^2A/(1 + cosA) = cosA`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
cos θ . sec θ = ?
Prove that sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A.
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
(1 – cos2 A) is equal to ______.
