Question

find the value cos²20+cos²65 whole divided by sin²40+sin²50 and
find the value sin20×cos70+cos20×sin70

Answer 1

Ans of que .2)

we know
sin(90-Ф)=cosФ
so...
sin20=cos70
so,
=sin20×cos70+cos20×sin70
=sin²20+cos²20
by pythagoras identity,
sin²+cos²=1
so
sin20×cos70+cos20×sin70=1
ans of que 1)
=(cos²20+cos²60)/(sin²40+sin²50)
we know
sin(90-Ф)=cosФ
so
=(cos²70+sin²70)(sin²50+cos²50)
by pythagoras identity,
sin²+cos²=1
so
=1/1
=1

Answer 2

$\frac{cos^220+cos^265}{sin^240+sin^250}= \frac{cos^220+cos^265}{sin^240+cos^240}= \frac{cos^220+cos^265}{1}$

$\frac{cos^220+cos^265}{1}= \frac{1.0616284167162193544398746203241}{1}$
used a calculator
as $sin^2x+cos^2x=1,sin(90-x)=cos(x)$
given x lies in first quadrant
$sin20(cos70)+sin70(cos(20))=$
$=(sin20)*(sin(90-70))+cos(20)(cos(90-70))=$
$sin^220+cos^220=1$