\(A=sin^215^o+sin^225^o+sin^235^o+sin^245^o+sin^255^o+sin^265^o+sin^275^o\)

\(A=cos^275^o+cos^265^o+cos^255^o+cos^245^o+sin^255^o+sin^265^o+sin^275^o\)

\(A=\left(cos^275^o+sin^275^o\right)+\left(cos^265^o+sin^265^0\right)+\left(cos^255^o+sin^255^o\right)+cos^245^o\)

\(A=1+1+1+0,5\)

\(A=3,5\)

a: \(A=sin^210^0+sin^280^0+cos^220^0+sin^270^0\)

\(=sin^210^0+cos^210^0+sin^270^0+sin^270^0\)

\(=2\cdot sin^270^0+1\)

b: \(=sin^215^0+sin^275^0+sin^235^0+sin^255^0\)

\(=sin^215^0+cos^215^0+sin^235^0+cos^235^0\)

=1+1

=2

\(A=sin^210^0+sin^280^0+cos^220^0+sin^270^0\)

\(=sin^210^0+cos^210^0+sin^270^0+sin^270^0\)

\(=2sin^270^0+1\)

\(B=sin^215^0+sin^275^0+sin^235^0+sin^255^0\)

\(=sin^215^0+cos^215^0+sin^235^0+cos^235^0\)

=1+1

=2

 Sửa lại đề bài là \(cos\left(15^o+2\alpha\right)\) (chứ không phải là \(cos^2\left(15^o+2\alpha\right)\) nhé)

 Ta có \(VT=sin^2\left(45^o+\alpha\right)-sin^2\left(30^o-\alpha\right)-sin15^o.cos^2\left(15^o+2\alpha\right)\)

\(=\left[sin\left(45^o+\alpha\right)+sin\left(30^o-\alpha\right)\right]\left[sin\left(45^o+\alpha\right)-sin\left(30^o-\alpha\right)\right]-sin15^ocos^2\left(15^o+2\alpha\right)\)

\(=2sin\left(\dfrac{75^o}{2}\right)cos\left(\dfrac{2\alpha+15^o}{2}\right).2cos\left(\dfrac{75^o}{2}\right)sin\left(\dfrac{2\alpha+15^o}{2}\right)-sin15^ocos^2\left(15^o+2\alpha\right)\)

\(=sin75^o.sin\left(2\alpha+15^o\right)-sin15^o.cos^2\left(2\alpha+15^o\right)\)

\(=sin\left(2\alpha+15^o-15^o\right)\) (dùng \(sin\left(\alpha-\beta\right)=sin\alpha.cos\beta-sin\beta.cos\alpha\))

\(=sin2\alpha=VP\)

Vậy đẳng thức được chứng minh.

Mấy chỗ kia bạn sửa hết \(cos^2\left(15^o+2\alpha\right)\) thành \(cos\left(15^o+2\alpha\right)\) nhé.

à ra r. k cần giải nha m.n