Question

verify the identity
1 + (sec^2)x *(sin^2)x = (sec^2)x

Answer 1

write something @kbarclay

Answer 2

can you substitute the one as cos^2x/cos^2x ?

Answer 3

ya

Answer 4

times both sides by cos^2. and simplify

Answer 5

u know\[\sec x=\frac{ 1 }{ \cos x }\]

Answer 6

yea so if I do that then cos^2x/ cos^2x + sin^2x/ cos^2x = sec^2x
which then can it be cos^2x +sin^2x/ cos^2x ?

Answer 7

sec^2 x * sin^2 x = sin^2 x/cos^2 x = tan^2 x
see your left side becomes,
1 + tan^2 x, this is an identity in trigo, that's is sec^2 x

LHS = RHS

Answer 8

thanks

Answer 9

\[1 + \sec^2x \times\sin^2x = \sec^2x\]
\[\qquad\qquad\qquad1 + \frac1{\cos^2x} \times\sin^2x = \frac1{\cos^2x}\\
~~~\cos^2x\times\left(1 + \frac1{\cos^2x} \times\sin^2x\right) = \cos^2x\times\frac1{\cos^2x}\\\qquad\qquad\qquad\qquad\qquad\quad\qquad=\]

Answer 10

wait how does that simplify to sec^2x=sec^2x @UnkleRhaukus

Answer 11

if you do it my way it should simplify to cos^2+sin^2=1

Answer 12

ok

Answer 13

so that would make it 1=1 since cos^2x+sin^2x = 1
and cos^2x/cos^2x =1

Answer 14

well yeah,

Answer 15

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