Question

7 cm đăng thức

a) \(\dfrac{tan\alpha-tan\beta}{cot\alpha-cot\alpha}=tan\alpha.cot\beta\)

b) \(tan100^o+\dfrac{sin530^o}{1+sin640^o}=\dfrac{1}{sin10^o}\)

c) 2(sin⁶α + cos⁶α) + 1 = 3(sin⁴α + cos⁴α)

Answer 1

c: 2(sin^6a+cos^6a)+1

=2[(sin^2a+cos^2a)^3-3*sin^2a*cos^2a]+1

=2-6sin^2acos^2a+1

=3-6*sin^2a*cos^2a

=3(sin^4a+cos^4a)

a:

Sửa đề: =-tana*tanb

 \(VT=\left(\dfrac{sina}{cosa}-\dfrac{sinb}{cosb}\right):\left(\dfrac{cosa}{sina}-\dfrac{cosb}{sinb}\right)\)

\(=\dfrac{sina\cdot cosb-sinb\cdot cosa}{cosa\cdot cosb}:\dfrac{cosa\cdot sinb-cosb\cdot sina}{sina\cdot sinb}\)

\(=\dfrac{sin\left(a-b\right)}{cosa\cdot cosb}\cdot\dfrac{sina\cdot sinb}{sin\left(b-a\right)}\)

\(=-tana\cdot tanb\)

=VP