Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
Advertisements
उत्तर
We know that,
`sin^2 A + cos^2 A = 1`
`sec^2 A - tan^2A = 1`
So
`sin^2 A + 1/(1 + tan^2 A) = sin^2 A + 1/sec^2 A`
`= sin^2 A + (1/sec A)^2`
`= sin^2 A + (cos A)^2`
`= sin^2 A + cos^2 A`
= 1
APPEARS IN
संबंधित प्रश्न
Evaluate sin25° cos65° + cos25° sin65°
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2 = 2`
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
Prove that sin4θ - cos4θ = sin2θ - cos2θ
= 2sin2θ - 1
= 1 - 2 cos2θ
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.
If `(cos alpha)/(cos beta)` = m and `(cos alpha)/(sin beta)` = n, then prove that (m2 + n2) cos2 β = n2
If cos θ = `24/25`, then sin θ = ?
Prove that `(1 + sintheta)/(1 - sin theta)` = (sec θ + tan θ)2
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
