Advertisements
Advertisements
Question
If sec θ = `25/7`, then find the value of tan θ.
Advertisements
Solution
∵ sec2θ – tan2θ = 1 ......[Identities]
`(25/7)^2 - ("tan" theta)^2 = 1`
`625/49 -1 = ("tan" theta)^2`
`(625 - 49)/49 = ("tan" theta)^2`
`576/49 = ("tan" theta)^2`
`"tan" theta = 24/7`
APPEARS IN
RELATED QUESTIONS
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
Prove that:
`cosA/(1 + sinA) = secA - tanA`
`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 tan10° tan 20° tan 70° tan 80° .
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
If tan α + cot α = 2, then tan20α + cot20α = ______.
