Advertisements
Advertisements
Question
If `sec theta = x ,"write the value of tan" theta`.
Advertisements
Solution
As , `tan^2 theta = sec^2 theta -1 `
So, `tan theta = sqrt( sec^2 theta -1 ) = sqrt( x^2 -1)`
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
Write the value of `(cot^2 theta - 1/(sin^2 theta))`.
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
9 sec2 A − 9 tan2 A is equal to
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Prove that (1 – cos2A) . sec2B + tan2B(1 – sin2A) = sin2A + tan2B
If cosA + cos2A = 1, then sin2A + sin4A = 1.
If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.
