Advertisements
Advertisements
Question
Prove that `(sin "A" - 2sin^3 "A")/(2cos^3 "A" - cos "A") = tan "A"`
Advertisements
Solution
Given
`(sin "A" - 2sin^2 "A")/(2cos^2 "A" - cos "A") = tan "A"`
L.H.S = `(sin "A" - 2 sin^3 "A")/(2 cos^3 "A" - cos "A")`
`= (sin "A" (1 - 2sin^2 "A"))/(cos "A" (2cos^2 "A" - 1))``
`= (sin"A"(sin^2 "A" + cos^2 "A" - 2sin^2 "A"))/(cos"A"(2cos^2"A" - sin^2 "A" - cos^2 "A"))`
`=(sin"A"(cos^2 "A" - sin^2 "A"))/(cos"A"(cos^2 "A" - sin^2 "A"))`
= `sin"A"/cos"A"`
= tan A
= R.H.S
Hence proved.
APPEARS IN
RELATED QUESTIONS
In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
State whether the following are true or false. Justify your answer.
cos A is the abbreviation used for the cosecant of angle A.
If `tan theta = a/b`, find the value of `(cos theta + sin theta)/(cos theta - sin theta)`
if `sec A = 17/8` verify that `(3 - 4sin^2A)/(4 cos^2 A - 3) = (3 - tan^2 A)/(1 - 3 tan^2 A)`
If `sin theta = a/b` find sec θ + tan θ in terms of a and b.
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
sin (45° + θ) – cos (45° – θ) is equal to ______.
Find will be the value of cos 90° + sin 90°.
Evaluate: 5 cosec2 45° – 3 sin2 90° + 5 cos 0°.
