Advertisements
Advertisements
Question
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
Advertisements
Solution
secθ + tanθ = `1/cosθ + sintheta/cosθ`
`=(1+sintheta)/costheta`
`=((1+sintheta)(1-sintheta))/(costheta (1-sintheta))`
`=(1^2 - sin^2theta)/(costheta(1-sintheta))`
`=cos^2theta/(costheta(1-sintheta))`
`therefore sectheta +tantheta =costheta/(1-sintheta)`
APPEARS IN
RELATED QUESTIONS
(secA + tanA) (1 − sinA) = ______.
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
Prove the following identities:
`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta )/(cos theta)`
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
If `sin theta = x , " write the value of cot "theta .`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Without using trigonometric identity , show that :
`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Prove that `(cot A)/(1 - tan A) + (tan A)/(1 - cot A) = 1 + tan A + cot A = sec A . "cosec" A + 1`.
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
