Advertisements
Advertisements
Question
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
Advertisements
Solution
`(sec theta -1)/( sec theta +1)`
= `((1/cos theta - 1/1))/((1/ costheta + 1/1))`
=`(((1- cos theta)/cos theta))/(((1+ cos theta)/cos theta))`
=`(1- cos theta)/(1+ cos theta)`
=`((1/1-2/3))/((1/1+2/3)`
=`((1/3))/((5/3))`
=`1/5`
APPEARS IN
RELATED QUESTIONS
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove the following identities:
`1/(secA + tanA) = secA - tanA`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
Write the value of `(1 + cot^2 theta ) sin^2 theta`.
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
9 sec2 A − 9 tan2 A is equal to
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ.
If 2sin2θ – cos2θ = 2, then find the value of θ.
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
