CORRECTION FOR NUMBER 2! THE PI SYMBOL DIDNT SHOW UP.
GIVEN: sin u = 3/5, 0 < u < pi/2
AND BTW, THAT "PLEASE SHOW ALL STEPS" IS FOR EACH PROBLEM. :)
sin 2x - sin x = 0
I assume from the questions, that you are familiar with the common identities.
Also you don't state a domain, so I will asuume 0 ≤ x ≤ 2pi
2sinxcos - sinx = 0
sinx(2cosx - 1) = 0
sinx = 0 or cosx = 1/2
from sinx = 0 , x = 0,pi,2pi
from cosx = 1/2, x must be in quadrants I or IV, so x = pi/3 or x = (2pi-pi/3) = 5pi/3
#2, you should recognize the 3,4,5 triangle and since u is in the first quadrant, cos u = 4/5 and tanu = 3/4
Now use your double angle formulas to find sin 2u etc.
Hint 15º = 45º - 30º
= sin45cos30 - cos45sin30
= √2/2(√3/2) - √2/2(1/2) = (√6 - √2)/4
always check these with a calculator
now do the cosine and the tangent in a similar way.
#4 hint: 195+105 = 300
195 - 105 = 90 mmmmhhhh!
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