CosA (tanA+2)(2tanA+1)=2secA+5sinA prove.... Pergunta de ideia deVinit

May 2019 1 130 Report

CosA (tanA+2)(2tanA+1)=2secA+5sinA prove

Lista de comentários

Verified answer

Bonjour ;

$cos(A) \big ( tan(A)+2\big ) \big (2tan(A)+1 \big ) = cos(A)\big( \dfrac{sin(A)}{cos(A)} +2\big )\big (2\dfrac{sin(A)}{cos(A)} + 1\big ) \\\\\\ = cos(A) \dfrac{sin(A)+2cos(A)}{cos(A)}\dfrac{2sin(A)+cos(A)}{cos(A)} \\\\\\ = \dfrac{\big(sin(A)+2cos(A)\big)\big(2sin(A)+cos(A)\big )}{cos(A)}$
$= \dfrac{2sin^2(A) +sin(A)cos(A) + 4cos(A)sin(A) + 2cos^2(A)}{cos(A)} \\\\\\ = \dfrac{2\big(sin^2(A)+cos^2(A)\big) +5sin(A)cos(A)}{cos(A)} = \dfrac{2 +5sin(A)cos(A)}{cos(A)} \\\\\\ =\dfrac{2}{cos(A)} + 5sin(A) = 2sec(A) + 5sin(A) \ .$

1 votes Thanks 0

Lista de comentários

Verified answer

Helpful Links

Helpful Social