Advertisements
Advertisements
प्रश्न
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
उत्तर
We have,
`sin A cos(90°-A)=sin A sin A+cos A cos A`
= `sin^2 A+cos ^2 A`
We know that, `sin^2 A+cos ^2 A`
Therefore,
\[\sin A\cos\left( 90°- A \right) + \cos A\sin\left( 90°- A \right) = 1\]
APPEARS IN
संबंधित प्रश्न
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
Prove that:
`cosA/(1 + sinA) = secA - tanA`
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
Write the value of tan1° tan 2° ........ tan 89° .
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2cosecθ`
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
Prove that sin4A – cos4A = 1 – 2cos2A
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`
Eliminate θ if x = r cosθ and y = r sinθ.