Verify each Identity

[shooterman]

cos^2x * tan^2x + sin^2x * tan^2x + 1 = sec^2x

 

[royhaas]

Start by simplifying the obvious with the tangents.

 

[shooterman]

as in getting cosx * sinex + cosx * sin^2x/cos ?
I am not sure on the right side of the plus sign

 

[Deleted member 4993]

cos^2x * tan^2x + sin^2x * tan^2x + 1 = sec^2x

cos[sup:12bbjemq]2[/sup:12bbjemq]x * tan[sup:12bbjemq]2[/sup:12bbjemq]x + sin[sup:12bbjemq]2[/sup:12bbjemq]x * tan[sup:12bbjemq]2[/sup:12bbjemq]x + 1

= tan[sup:12bbjemq]2[/sup:12bbjemq](x) * [cos[sup:12bbjemq]2[/sup:12bbjemq](x) + sin[sup:12bbjemq]2[/sup:12bbjemq](x)] + 1

Now continue.....

 

[shooterman]

cos^2x * tan^2x + sin^2x * tan^2x + 1 = sec^2x

cos[sup:2h03t5jx]2[/sup:2h03t5jx]x * tan[sup:2h03t5jx]2[/sup:2h03t5jx]x + sin[sup:2h03t5jx]2[/sup:2h03t5jx]x * tan[sup:2h03t5jx]2[/sup:2h03t5jx]x + 1

= tan[sup:2h03t5jx]2[/sup:2h03t5jx](x) * [cos[sup:2h03t5jx]2[/sup:2h03t5jx](x) + sin[sup:2h03t5jx]2[/sup:2h03t5jx](x)] + 1

Now continue.....

Can you explain how you got to that please thx.

 

[Deleted member 4993]

cos^2x * tan^2x + sin^2x * tan^2x + 1 = sec^2x

cos[sup:1tvvviyn]2[/sup:1tvvviyn]x * tan[sup:1tvvviyn]2[/sup:1tvvviyn]x + sin[sup:1tvvviyn]2[/sup:1tvvviyn]x * tan[sup:1tvvviyn]2[/sup:1tvvviyn]x + 1

= tan[sup:1tvvviyn]2[/sup:1tvvviyn](x) * [cos[sup:1tvvviyn]2[/sup:1tvvviyn](x) + sin[sup:1tvvviyn]2[/sup:1tvvviyn](x)] + 1

Now continue.....

Can you explain how you got to that please thx.<<< factored out the common factor [tan[sup:1tvvviyn]2[/sup:1tvvviyn](x)]

 

[shooterman]

you explain how you got to that please thx.<<< factored out the common factor [tan2(x)]

Didn't quite get that yet sorry, but i do understanted this tan2(x) * [cos2(x) + sin2(x)] + 1
cos2(x) + sin2(x) = 1 so..

tan2(x) * (1) +1 = tan[sup:3inm74h2]2[/sup:3inm74h2]x + 1 = sec[sup:3inm74h2]2[/sup:3inm74h2]x