Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
sin2 A cot2 A + cos2 A tan2 A = 1
उत्तर
We have to prove `sin^2 A cot^2 A + cos^2 A tan^2 A = 1`
We know that `sin^2 A + cos^2 A = 1`
So,
`sin^2 A cot^2 A + cos^2 A tan^2 A = sin^2 A (cos^2 A)/(sin^2 A) + cos^2 A(sin^2 A)/(cos^2 A)`
`= cos^2 A + sin^2 A`
= 1
APPEARS IN
संबंधित प्रश्न
If (secA + tanA)(secB + tanB)(secC + tanC) = (secA – tanA)(secB – tanB)(secC – tanC) prove that each of the side is equal to ±1. We have,
Prove the following trigonometric identities.
`tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + tan theta + cot theta`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
If tan θ = `9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ......[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.
