Question

please help! i really don't understand trigonometry

Answer 1

A ). ${sin} ^{2}x$ - 2 sinx cos x + ${cos} ^{2}x$

L. H. S. = ${(sinx \: - \: cos x) } ^{2}x$

= ${sin} ^{2}x$ - 2 sinx cos x + ${cos} ^{2}x$

= ${sin} ^{2}x$ + ${cos} ^{2}x$ - 2 sinx cos x

= 1 - 2 sinx cos x

= ${sec} ^{2}x$ - ${tan} ^{2}x$ - 2 sinx cos x

=> R. H. S.

$\sf{\underline {Identity\: Used}}$:

⚫${\tt{(\:a \: - \:b\:)} ^{2}} x$ = ${\tt{a} ^{2}} x$ + ${\tt{b} ^{2}} x$ - 2 ab

⚫1 + ${\tt {tan} ^{2}} x$ = ${\tt {sec} ^{2}} x$