Question

1)1/49 в степени -x/2=7
2)Упростите tga+tgb/tga-tgb

Answer 1

1) $frac{1}{49}^{frac{-x}{2}} = 7$
$(7^{-2})^{frac{-x}{2}} = 7^{1}$
$7^{frac{-2*(-x)}{2}} = 7^{1}$
$7^{x} = 7^{1}$
$x = 1$

2) (tga + tgb)/ (tga - tgb) ; Пусть (tga + tgb) = A  и (tga - tgb) = B

A = sina/cosa + sinb/cosb = [sina*cosb + sinb*cosa]/ cosa*cosb =
= sin(a+b)/cosa*cosb

B = sina/cosa - sinb/cosb = [sina*cosb - sina*cosa]/cosa*cosb* = 
=sin(a-b)/cosa*cosb

A/B = sin(a+b)/cosa*cosb : sin(a-b)/cosa*cosb = sin(a+b)/sin(a-b)