Advertisements
Advertisements
प्रश्न
If `m = (cos θ - sin θ)` and `n = (cos θ + sin θ)`, show that `sqrt(m/n) + sqrt(n/m) = 2/sqrt(1 - tan^2θ)`.
Advertisements
उत्तर
LBS = `sqrt(m/n) + sqrt(n/m)`
= `sqrt(m)/sqrt(n) + sqrt(n)/sqrt(m)`
= `(m+n)/sqrt(mn)`
= `((cos theta - sin theta) + (cos theta + sin theta))/sqrt((cos theta - sin theta)(cos theta + sin theta))`
= `(2 cos theta)/ sqrt(cos ^2 theta - sin^2 theta)`
= `((( 2 cos theta)/(cos theta)))/((sqrt(cos^2 theta - sin^2 theta)/(cos theta))`
= `2/(sqrt((cos^2 theta)/(cos^2 theta) - (sin^2 theta)/(cos^2 theta))`
= `2/sqrt(1- tan^2 theta)`
= RHS
APPEARS IN
संबंधित प्रश्न
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Prove the following trigonometric identities:
(1 – cos2 A) cosec2 A = 1
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
Write the value of tan1° tan 2° ........ tan 89° .
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
Find the value of sin 30° + cos 60°.
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
