Advertisements
Advertisements
प्रश्न
Prove that (1 + cot θ – cosec θ)(1+ tan θ + sec θ) = 2
Advertisements
उत्तर
L.H.S =(1 + cot θ – cosec θ)(1+ tan θ + sec θ)
= `(1 + costheta/sintheta - 1/sin theta)(1+sin theta/cos theta + 1/cos theta)`
`= ((sintheta + costheta - 1)/sintheta)((costheta + sintheta +1)/costheta)`
`= 1/(sinthetacostheta) ((sinthetacostheta+sin^2theta + sin theta+cos^2theta),(+sinthetacostheta+costheta-costheta - sin theta -1))`
`= 1/(sinthetacostheta) (2sinthetacostheta + (sin^2theta + cos^2 theta) - 1)`
`= 1/(sin thetacostheta) (2sinthetacostheta + 1 - 1)`
`= (2sin thetacostheta)/(sin thetacos theta)`
= 2
= R.H.S
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
If cos θ = `24/25`, then sin θ = ?
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
