Advertisements
Advertisements
प्रश्न
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
उत्तर
`cos^2theta + cos theta =1`
LHS = `cos^2 theta + cos theta`
=`1- sin^2 theta + cos theta `
=` 1- ( sin^2 theta - cos theta )`
Since LHS ≠ RHS, this not an identity.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
If tanθ + sinθ = m and tanθ – sinθ = n, show that `m^2 – n^2 = 4\sqrt{mn}.`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
`cot^2 theta - 1/(sin^2 theta ) = -1`a
cosec4θ − cosec2θ = cot4θ + cot2θ
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
What is the value of (1 + cot2 θ) sin2 θ?
\[\frac{x^2 - 1}{2x}\] is equal to
The value of sin2 29° + sin2 61° is
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then
If cos A + cos2 A = 1, then sin2 A + sin4 A =
If `x/(a cosθ) = y/(b sinθ) "and" (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that" x^2/a^2 + y^2/b^2 = 1`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
If sec θ = `25/7`, then find the value of tan θ.
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Prove that `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
