Điền vào chỗ trống {......}để đơn giản các biểu thức sau:
a)\(\dfrac{ }{ }\) 1 + tan\(^2\) a =1 +\((\dfrac{...}{...})\)2 =\(\dfrac{....+....}{cos^2a}=\dfrac{........}{cos^2a}\)
b) 1 + cot2 a= + \((\dfrac{...}{...})^2\) = \(\dfrac{....+....}{sin^2a}=\dfrac{....}{sin^2a}\)
c) tan2 a (2 sin2a + 3 cos2 a - 2)
=tan2 a[cos2 a +2 (........ +.........)-2 ]
=\(\dfrac{sin^2a}{cos^2a}\)\(\times\)........=........
a) 1 + tan22 a =1 +(\(\dfrac{sina}{cosa}\))2 =\(\dfrac{sina+cosa}{cos^2a}\)=\(\dfrac{1}{cos^2a}\)
b) 1 + cot2 a= 1 +(\(\dfrac{cosa}{sina}\))2 = \(\dfrac{cosa+sina}{sin^2a}\)=\(\dfrac{1}{sin^2a}\)
c) tan2 a (2 sin2a + 3 cos2 a - 2)
=tan2 a[cos2 a +2 (\(sina^2+cos^2a\))-2 ]
=\(\dfrac{sin^2a}{cos^2a}\)×\(cos^2a=sin^2a\)
b: \(1+cot^2a=1+\left(\dfrac{cosa}{sina}\right)^2=\dfrac{1}{sin^2a}\)
c: \(=tan^2a\left[2\left(1-cos^2a\right)+3cos^2a-2\right]\)
\(=tan^2a\left[cos^2a\right]\)
\(=\dfrac{sin^2a}{cos^2a}\cdot cos^2a=sin^2a\)
