Advertisements
Advertisements
Question
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
Advertisements
Solution
`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
RELATED QUESTIONS
Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
Prove the following trigonometric identities.
`cosec theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
`(cos ec^theta + cot theta )/( cos ec theta - cot theta ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta cot theta`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
If \[\sin \theta = \frac{1}{3}\] then find the value of 9tan2 θ + 9.
cos4 A − sin4 A is equal to ______.
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Prove that cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.
Prove that `(sin^2theta)/(cos theta) + cos theta` = sec θ
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
Prove that `"cot A"/(1 - cot"A") + "tan A"/(1 - tan "A")` = – 1
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
