Advertisements
Advertisements
प्रश्न
If m = ` ( cos theta - sin theta ) and n = ( cos theta + sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.
Advertisements
उत्तर
LBS = `sqrt(m/n) + sqrt(n/m)`
=`sqrt(m)/sqrt(n) + sqrt(m)/sqrt(n)`
=`(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 ) / sqrt( cos ^ theta - sin^ 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
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
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 the following trigonometric identities
`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Without using the trigonometric table, prove that
tan 10° tan 15° tan 75° tan 80° = 1
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
If tan α + cot α = 2, then tan20α + cot20α = ______.
