Advertisements
Advertisements
प्रश्न
Prove that `sqrt((1 + cos A)/(1 - cos A)) = "cosec" A + cot A`.
Advertisements
उत्तर
L.H.S. = `sqrt((1 + cos A)/(1 - cos A))`
= `sqrt((1 + cos A)/(1 - cos A) xx (1 + cos A)/(1 + cos A))` ...[On rationalising the denominator]
= `sqrt((1 + cos A)^2/(1 - cos^2 A))`
= `sqrt((1 + cos A)^2/(sin^2 A)` ...`[(∵ sin^2A + cos^2A = 1),(∴ 1 - cos^2A = sin^2A)]`
= `(1 + cos A)/(sin A)`
= `1/(sin A) + (cos A)/(sin A)`
= cosec A + cot A
= R.H.S.
∴ `sqrt((1 + cos A)/(1 - cos A)) = "cosec" A + cot A`
APPEARS IN
संबंधित प्रश्न
If (secA + tanA)(secB + tanB)(secC + tanC) = (secA – tanA)(secB – tanB)(secC – tanC) prove that each of the side is equal to ±1. We have,
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove that:
`cosA/(1 + sinA) = secA - tanA`
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
If (tan θ + sin θ) = m and (tan θ – sin θ) = n, prove that (m2 – n2)2 = 16 mn.
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
Prove the following identity :
`(1 - tanA)^2 + (1 + tanA)^2 = 2sec^2A`
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Find the value of sin 30° + cos 60°.
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Without using the trigonometric table, prove that
tan 10° tan 15° tan 75° tan 80° = 1
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
