Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
sin2 A cot2 A + cos2 A tan2 A = 1
Advertisements
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 secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
Prove the following trigonometric identities.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
Prove that:
(cosec A – sin A) (sec A – cos A) sec2 A = tan A
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
Choose the correct alternative:
1 + tan2 θ = ?
Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Prove that `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
sin2θ + sin2(90 – θ) = ?
Prove that cosec θ – cot θ = `sin theta/(1 + cos theta)`
