Advertisements
Advertisements
प्रश्न
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
Advertisements
उत्तर
LHS = `sin^2 theta + cos ^4 theta`
=`sin^2 theta + ( cos ^2 theta )^2`
=`sin^2 theta + (1- sin^2 theta)^2`
=` sin^2 theta + 1 -2 sin^2 theta + sin ^4 theta`
=`1-sin^2 theta + sin^4 theta`
=`cos^2 theta + sin^4 theta`
= RHS
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
`(1+tan^2A)/(1+cot^2A)` = ______.
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
If `(cosec theta - sin theta )= a^3 and (sec theta - cos theta ) = b^3 , " prove that " a^2 b^2 ( a^2+ b^2 ) =1`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
Prove that 2(sin6A + cos6A) – 3(sin4A + cos4A) + 1 = 0.
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
If 2sin2θ – cos2θ = 2, then find the value of θ.
(1 – cos2 A) is equal to ______.
