Question

5. Đơn giản biểu thức a , cos a - cos a × sin^2 a b , sin^6 a + cos^6 a + 3sin^2 a 6. Tính giá trị của biểu thức. a, A= sin^2 54°-cos^2 30° + sin^2 36° + tận 45° b, B= 1-sin^2 43°/ cos^2 43° c, C= sin^4 a - cos^4 a / sin^2 a - cos^2 a

Answer 1

a.

\(cosa-cosa.sin^2a=cosa.\left(1-sin^2a\right)=cosa.cos^2a=cos^3a\)

b.

\(sin^6a+cos^6a+3sin^2a=\left(sin^2a+cos^2a\right)^2-3sin^2acos^2a.\left(sin^2a+cos^2a\right)+3sin^2a\)

\(=1-3sin^2a.cos^2a+3sin^2a\)

\(=1+3sin^2a\left(1-cos^2a\right)=1+3sin^2a.sin^2a\)

\(=1+3sin^4a\)

Answer 2

6.

\(A=sin^254-cos^230+sin^236+tan^245\)

\(=sin^254-\left(\dfrac{\sqrt{3}}{2}\right)^2+sin^2\left(90-54\right)+1^2\)

\(=sin^254+cos^254-\dfrac{3}{4}+1\)

\(=1-\dfrac{3}{4}+1=\dfrac{5}{4}\)

\(B=\dfrac{1-sin^243}{cos^243}=\dfrac{cos^243}{cos^243}=1\)

\(C=\dfrac{sin^4a-cos^4a}{sin^2a-cos^2a}=\dfrac{\left(sin^2a-cos^2a\right)\left(sin^2a+cos^2a\right)}{sin^2a-cos^2a}\)

\(=sin^2a+cos^2a=1\)