Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
Advertisements
рдЙрддреНрддрд░
We have x = a `cos^3 theta `
= > `x/a = cos^3 theta ........(i)`
Again , `y = b sin^3 theta`
= > `y/b = sin^3 theta .....(ii)`
Now , LHS = `(x/a)^(2/3) + (y/b)^(2/3)`
= `( cos^3 theta )^(2/3) + (sin^3 theta )^ (2/3 )` [ from (i) and (ii)]
=` cos^2 theta + sin^2 theta `
=1
ЁЭР╗ЁЭСТЁЭСЫЁЭСРЁЭСТ, ЁЭР┐ЁЭР╗ЁЭСЖ = ЁЭСЕЁЭР╗ЁЭСЖ
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following trigonometric identities.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Prove that:
2 sin2 A + cos4 A = 1 + sin4 A
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to
If x = a sec θ cos ╧Х, y = b sec θ sin ╧Х and z = c tan θ, then\[\frac{x^2}{a^2} + \frac{y^2}{b^2}\]
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
If tan θ = `13/12`, then cot θ = ?
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ
If cosA + cos2A = 1, then sin2A + sin4A = 1.
