Question

can someone help me with this
1 + sec^2(x) sin^2(x) = sec^2(x)

Answer 1

prove the equation

Answer 2

1+ sec^2 (x) [1 +cos^2 (x)] = sec^2 (x)
1+ sec^2(x) + sec^2 (x) .cos^2 (x) = sec^2 (x)
1+ sec^2(x) =sec^2 (x)

is yur question correct?

Answer 3

hold on

Answer 4

sin^2(x) doesnt equal 1+cos^2 (x) it equals 1-cos^2(x)

Answer 5

1 + sec^2 . sin^2 = sec^2

1 + 1/cos^2 . sin^2 = sec^2

1 + sin^2/cos^2 = sec^2

1 + tan^2 = sec^2

Answer 6

thanks dude

Answer 7

Which is an identity.
_ _ _

[if you want to do it another way]

1 + sec^2(x) sin^2(x) = sec^2(x)

1 + 1/cos^2 . sin^2 =1/cos^2

cos^2 + sin^2 = 1

Which might be a more familiar identity .

Answer 8

convert sec^2(x) into 1/cos^2(x)

1+tan^2(x)
Hence proved
1+tan^2(x) = sec^2(x)
Any questions ?

Answer 9

@Haseeb96 's method would have worked too,

1+ sec^2 [1 - cos^2] = sec^2
1+ sec^2 - cos^2sec^2 = sec^2

1+ sec^2 - cos^2/cos^2 = sec^2
1+ sec^2 - 1 = sec^2
sec^2 = sec^2

Answer 10

thanks