Advertisements
Advertisements
प्रश्न
Prove that `sqrt((1 + cos "A")/(1 - cos"A"))` = cosec A + cot A
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")` ......`[(because sin^2"A" + cos^2"A" = 1),(therefore 1 - cos^2"A" = sin^2"A")]`
= `(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 cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
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.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA cosecA + 1`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
(sec A + tan A) (1 − sin A) = ______.
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Choose the correct alternative:
1 + cot2θ = ?
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
