Advertisements
Advertisements
प्रश्न
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
Advertisements
उत्तर
(1 + tan A + sec A) (1 + cot A – cosec A)
= 1 + cot A – cosec A + tan A + 1 – sec A + sec A + cosec A – cosec A sec A
= `2 + cosA/sinA + sinA/cosA - 1/(sinAcosA)`
= `2 + (cos^2A + sin^2A)/(sinAcosA) - 1/(sinAcosA)`
= `2 + 1/(sinAcosA) - 1/(sinAcosA)`
= 2
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
`cot^2 theta - 1/(sin^2 theta ) = -1`a
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
What is the value of 9cot2 θ − 9cosec2 θ?
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
