Question

If sin A , cos A , tan A are in Geometric Progression . then cos^3A+cos^2A = ??

Answer 1

well what does a geometric progression tell us about how the terms are formed?

Answer 2

cos a=rsina
tan a=r^2sina

Answer 3

correct, another way to look at it may be from the center out in this case:

sin, sin cot, sin cot cot (= tan)

Answer 4

had some competing thoughts lol

Answer 5

cos tan = sin
cos = cos
cos sin/cos^2 = tan

Answer 6

sin/cos^2 needs to equal cot giving us cos^2 = sin tan

Answer 7

.... need paper lol

Answer 8

cos^3+cos^2

cos^2(cos + 1)

(1-sin^2)(cos + 1)

(1 + sin) (1 - sin) (cos + 1)

just some reworkings to try to get it into some useable format

Answer 9

is there any more context to the question? any idea as to what its looking for as a solution? is it a proof, or something else?

Answer 10

do we need to solve for A?

Answer 11

answer is given as 1. thats about it.
we need to find cos^2A+cos^3A if sin,cos, tan are in gp

Answer 12

yeah, solving for A is paramount then

Answer 13

sinA * r = cosA if r = cot(A)

sinA*r^2 = tanA if r^2 = secA

or a geometric mean might help too

cosA = sqrt(sinA tanA)

cos^2A = sin^2A/cosA

cos^3A = sin^2A

cos^3A = 1 - cos^2A

got it

Answer 14

ohohoh. yeah. didnt see that. i was trying to break down cos^2 A simultaneously. xD
Thankyouu. :)

Answer 15

youre welcome .... the geometric mean made this much simpler