Advertisements
Advertisements
प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Advertisements
उत्तर
L.H.S
= `(cosec θ – cot θ)^2`
= `(1/sintheta - costheta/sintheta)^2`
= `(1-costheta)^2/(sin^2 theta)`
= `(1-cos theta)^2/(1-cos^2theta)`
= `((1-costheta)(1-costheta))/((1-costheta)(1+cos theta)) `
= `(1-cos theta)/(1+costheta)`
= R.H.S
संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
What is the value of (1 − cos2 θ) cosec2 θ?
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
If x = a tan θ and y = b sec θ then
If cos θ = `24/25`, then sin θ = ?
Prove that
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A
Show that tan 7° × tan 23° × tan 60° × tan 67° × tan 83° = `sqrt(3)`
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
