Advertisements
Advertisements
Question
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Advertisements
Solution
We have to prove `1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
We know that, `sin^2 A + cos^2 A = 1`
So,
`1/(1 + sin A) + 1/(1 - sin A) =((1 - sin A) + (1 + sin A))/((1 + sin A)(1 - sin A))`
`= (1 - sin A + 1+ sin A)/(1 - sin^2 A)`
`= 2/cos^2 A`
`= 2 sec^2 A`
APPEARS IN
RELATED QUESTIONS
If `sec alpha=2/sqrt3` , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.
Prove the following trigonometric identities.
`"cosec" theta sqrt(1 - cos^2 theta) = 1`
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
What is the value of \[6 \tan^2 \theta - \frac{6}{\cos^2 \theta}\]
sec4 A − sec2 A is equal to
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
Without using trigonometric identity , show that :
`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`
Prove that:
`sqrt(( secθ - 1)/(secθ + 1)) + sqrt((secθ + 1)/(secθ - 1)) = 2 "cosec"θ`
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
`(1 + cot^2A)/(1 + tan^2A)` = ?
If 4 tanβ = 3, then `(4sinbeta-3cosbeta)/(4sinbeta+3cosbeta)=` ______.
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
