Advertisements
Advertisements
Questions
`sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`
Prove the following:
`sqrt((1 + sin θ)/(1 - sin θ)) = (sec θ + tan θ)`
Advertisements
Solution
LHS = `sqrt((1 + sin θ)/(1 - sin θ))`
=`sqrt(((1 + sin θ))/(1 - sin θ) xx ((1 + sin θ))/(1 + sin θ))`
=` sqrt(((1 + sin θ)^2)/(1 - sin^2 θ))`
=`sqrt(((1 + sin θ)^2)/(cos^2 θ))`
=`(1 + sin θ)/cos θ`
=`1/cos θ + (sin θ)/(cos θ)`
= sec θ + tan θ
= RHS
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`
[Hint: Write the expression in terms of sinθ and cosθ]
Prove the following trigonometric identities.
`(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
`cot^2 theta - 1/(sin^2 theta ) = -1`a
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt(a^2 + b^2 - c^2)`
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`
