SOLUTION: Use the trigonometric identities to expand and simplify if possible. For 1−cos(𝐷)/sin(𝐷)+1 sin(270-A) = cos(B+270)= tan(C+225)

Algebra ->  Trigonometry-basics -> SOLUTION: Use the trigonometric identities to expand and simplify if possible. For 1−cos(𝐷)/sin(𝐷)+1 sin(270-A) = cos(B+270)= tan(C+225)      Log On


   

Question 1151108: Use the trigonometric identities to expand and simplify if possible.
For 1−cos(𝐷)/sin(𝐷)+1
sin(270-A) =
cos(B+270)=
tan(C+225)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Use the trigonometric identities to expand and simplify if possible.
For:
%281-cos%28D%29%29%2F%28sin%28D%29%2B1%29-> cannot be simplified


sin%28270-A%29 = ...........Use the following identity : sin+%28s-t%29=-cos++%28s%29%2Asin%28t+%29%2B+cos%28t%29%2Asin%28s%29
sin%28270-A%29+=-+cos+%28270%29+%2Asin%28A%29%2B+cos%28A%29%2Asin%28270%29...........since cos%28270%29=0+and sin%28270%29=-1, we have
sin%28270-A%29+=-+0%2Asin++%28A+%29%2B+cos+%28A+%29+%2A%28-1%29
sin%28270-A%29+=0-+cos+%28A+%29+
sin%28270-A%29+=-+cos+%28A+%29+

for next one use identities above
cos%28B%2B270%29=cos%28270%29cos%28B%29+-+sin%28270%29+sin%28B%29
cos%28B%2B270%29=0%2A+cos%28B%29+-%28-1%29+sin%28B%29
cos%28B%2B270%29=+sin%28B%29


tan%28C%2B225%29=............Use the following identity : tan%28a%29=sin%28a%29%2Fcos%28a%29
tan%28C%2B225%29=sin%28C%2B225%29%2Fcos%28C%2B225%29

since sin%28225%29=-1%2Fsqrt%282%29+and cos%28225%29=-1%2Fsqrt%282%29, we have




tan%28C%2B225%29=%28+sin%28C%29%2B+cos%28C%29++%29%2F++%28sin%28C%29+-++cos%28C%29%29