Trigonometrical identities.?

Question

Does anyone can help me with it???

Using trigonometrical identities find the general solutions in degree

a)sinx=cosx

b)cos^2x=1

c)tanx=cosecx

d)sin^2x-1/4=0

e)2sin2x-cos2x=1

f)(tan2x)(tanx)=2

g)3cos^2x-2sinx-2=0

h)2cos^2x-sinx-1=0

Thanks

I still have problem with these:

c)tanx=cosecx

d)sin^2x-1/4=0

e)sin2x-cos2x=1

f)(tan2x)(tanx)=2

Step by step would be nice :o)

Answer 1

sin x = cos x at 45 and 225 degrees (pi/4 and 5 pi/4 and multiples of them)

cos^2 x = 1 when sin x =0 (multiples of pi)

tax x = csc x when sin x = 1 ( pi/2 and multiples)

sin^2 x = 1/4 when sin x = 1/2 (pi/6 and multiples)

e) when sin 2x = cos 2x (pi/4 and multiples)

f) when tan x = 1 (pi/4 and 5pi/4 and multiples)

etc..

using identities:

sin(pi/2 - x) = cos x.... pi/2 - x = x when x = pi/4

sin^2 x + cos^2 x =1 .... 0 + cos^2x =1.... sin^2 x = 0

sin x /cos x = 1/cos x when sin x =1

etc

Answer 2

I'm not going to do the whole lot but will give you some pointers.
a) divide both sides by cosx to get sinx/cosx = 1 so tanx = 1
b) subtract cos^2x from both sides to get 0 = 1 - cos^2x
so 0 = sin^2x
d) and the next few involve breaking up the double angles and then factorising.

Answer 3

If you ask questions one by one, then you can get all the answers.

Here I start the first couple of problems:
a) sinx=cosx=sin(90-x+360n)
x = 90-x+360n
x = 45+180n, degrees
where n can be any integer.

b)cos^2x=1
cosx = ±1
x = 180n, degrees
where n can be any integer.

Answer 4

Are you beneficial tah theta = 25 stages? no longer 25 in basic terms? For something I shall use T for theta 2d, value = -cos30 = cos(a hundred and eighty-30) or cos(a hundred and eighty+30) so T = a hundred and fifty or 210. third, sinT = -sin80 = sin(a hundred and eighty+80) 0r sin(360-80) for this reason T = 260 of 280. Fourth, tanT = -tan15 = tah(a hundred and eighty-15) or tan(360-15) so T = one hundred sixty five or 345. it form of feels you haven't any longer carried out Trig ratios of allied angles.

Answer 5

i second this question
im on the same math and its friggin hard
but you should post the formulas so that ppl can try and figure out how to do it