Sin^2(п-t)/1+sin(3п/2+t)=cos(2п-t)

Предыдущий
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вопрос

To simplify the expression sin^2(п-t)/(1+sin(3п/2+t)), we can use trigonometric identities to rewrite sin^2(п-t) and sin(3п/2+t) in terms of cosine functions:

sin^2(п-t) = (1 - cos(2(п-t)))/2
sin(3п/2+t) = -cos(3п/2+t)

Now, let's substitute these into the expression:

(1 - cos(2(п-t)))/2 / (1 - cos(3п/2+t)) = cos(2п-t)

We can simplify the expression further by using the angle addition formula for cosine:

cos(2(п-t)) = cos(2п)cos(t) + sin(2п)sin(t) = cos(t)

Therefore, the simplified expression is:

(1 - cos(t))/2 / (1 + cos(t)) = cos(2п-t)

This is the simplified form of the given expression.