Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Advertisements
उत्तर
We know that `sin^2 theta + cos^2 theta = 1`
Multiplying both numerator and the denominator by `(1 - sin theta)`, we have
`cos theta/(1 + sin theta) = (cos theta(1 - sin theta))/((1 + sin theta)(1 - sin theta))`
`= (cos theta(1 - sin theta))/(1 - sin^2 theta)`
`= (cos theta (1 - sin theta))/cos^2 theta`
`= (1 - sin theta)/cos theta`
APPEARS IN
संबंधित प्रश्न
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
`(1-cos^2theta) sec^2 theta = tan^2 theta`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
What is the value of \[6 \tan^2 \theta - \frac{6}{\cos^2 \theta}\]
Write True' or False' and justify your answer the following :
The value of \[\cos^2 23 - \sin^2 67\] is positive .
sec4 A − sec2 A is equal to
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
If sec θ = `25/7`, find the value of tan θ.
Solution:
1 + tan2 θ = sec2 θ
∴ 1 + tan2 θ = `(25/7)^square`
∴ tan2 θ = `625/49 - square`
= `(625 - 49)/49`
= `square/49`
∴ tan θ = `square/7` ........(by taking square roots)
Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
