How do you simplify the following expression? \(\displaystyle{Q}={\left({1}-{{\tan}^{{2}}{\left({x}\right)}}\right)}{\left({1}-{{\tan}^{{2}}{\left({\frac{{{x}}}{{{2}}}}\right)}}\right)}\cdots{\left({1}-{{\tan}^{{2}}{\left({\frac{{{x}}}{{{2}^{{n}}}}}\right)}}\right)}\)

Trent Fuller

Trent Fuller

Answered question

2022-04-09

How do you simplify the following expression?
Q=(1tan2(x))(1tan2(x2))(1tan2(x2n))

Answer & Explanation

Buizzae77t

Buizzae77t

Beginner2022-04-10Added 13 answers

Hint:
1tan2t=cos2tsin2tcos2t=cos(2t)cos2t
and for arguments of the form x2n, many things will vanish in the product.

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