Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identity:
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
Advertisements
उत्तर
`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`
LHS = `sqrt((1 + sin A)/(1 - sin A)`
Rationalize the numerator abd denominator with `sqrt(1 + sin A)`
LHS = `sqrt(((1 + sin A)(1 + sin A))/((1 - sin A)(1 + sin A)))`
= `sqrt((1 + sin A)^2/(1 - sin^2 A))`
= `sqrt((1 + sin A)^2/(cos^2 A))`
= `(1 + sin A)/(cos A)`
= `1/(cos A) + (sin A)/(cos A)`
= sec A + tan A
= RHS
APPEARS IN
संबंधित प्रश्न
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 identities:
cot2 A – cos2 A = cos2 A . cot2 A
Show that : tan 10° tan 15° tan 75° tan 80° = 1
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
If 4 cos2 A – 3 = 0, show that: cos 3 A = 4 cos3 A – 3 cos A
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`(1+ cos theta + sin theta)/( 1+ cos theta - sin theta )= (1+ sin theta )/(cos theta)`
If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
Prove the following identity :
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ
cos 45° = ?
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
