Rearranging an expression in sqrt argument

[tomwilliam]

Homework Statement

Rearranging an equation...can't quite see how it's done.

Homework Equations

$$r=\sqrt{2.5^{2}cos^{2}(t/2)+5^{2}sin^{2}(t/2)}$$
$$r=2.5\sqrt{cos^{2}(t/2)+4sin^{2}(t/2)}$$
$$r=2.5\sqrt{1+3sin^{2}(t/2)}$$

The Attempt at a Solution

I know that $$cos^{2}(x)+sin^{2}(x)=1$$ but that gives me the (wrong) answer
$$r=2.5\sqrt{1+24sin^{2}(t/2)}$$

It should be simple, but I'm obviously doing something wrong. Any help appreciated.

 

[BAdhi]

The Attempt at a Solution

I know that $$cos^{2}(x)+sin^{2}(x)=1$$ but that gives me the (wrong) answer
$$r=2.5\sqrt{1+24sin^{2}(t/2)}$$

are you sure that you've substituted correctly
'cause
$$cos^2(t/2)+4sin^{2}(t/2)= (1-sin^{2}(t/2))+4sin^2(t/2)=1+3sin^2(t/2)$$

 

[tomwilliam]

Thanks
I'm fine getting from my second line to my third line, following the same logic as you have presented. My problem is how to get from the first line, to the expression with cos squared plus 4 sin squared in the sqrt.

 

[tomwilliam]

It's ok, I've figured it out now. Thanks for your help

 

[BAdhi]

why,
$$\sqrt{2.5^2cos^2(t/2)+(2.5)^2.2^2sin^2(t/2)} = 2.5\sqrt{cos^2(t/2)+2^2sin^2(t/2)}$$