# trigonometry equationsss =(

• July 25th 2009, 04:30 AM
iiharthero
trigonometry equationsss =(
hii guyz, i would REALLY like some help for these trig equation questions
thank you sooo much if you can helpp me !

if secx - tanx = 3/5, show that sinx = 8/17

if tanx = t, express sin2x and cos2x in terms of t. Find the values for t for which

(k+1)sin2x + (k-1)cos2x = k+1

thankyouuuu againn !!
• July 25th 2009, 04:57 AM
running-gag
Quote:

Originally Posted by iiharthero
hii guyz, i would REALLY like some help for these trig equation questions
thank you sooo much if you can helpp me !

if secx - tanx = 3/5, show that sinx = 8/17

Hi

$\sec x - \tan x = \frac35 \implies \frac{1-\sin x}{\cos x} = \frac 35$ $\implies 5(1-\sin x) = 3 \cos x$

Square both sides and substitute cos²x with 1-sin²x to find a quadratic in sin x, one of the solutions being "impossible" the other one is the good one
• July 25th 2009, 08:31 AM
red_dog
Quote:

Originally Posted by iiharthero

if tanx = t, express sin2x and cos2x in terms of t. Find the values for t for which

(k+1)sin2x + (k-1)cos2x = k+1

$\sin 2x=\frac{2\tan x}{1+\tan^2x}, \ \cos 2x=\frac{1-\tan^2x}{1+\tan^x}$