## anonymous 5 years ago If $\tan(\frac \pi 2 \sin a)=\cot(\frac \pi 2 \cos a)$ then cos a +sin a =

1. anonymous

1

2. anonymous

i got that too. but the answer is -1

3. anonymous

no wait it says.. it could be 1 or -1

4. anonymous

do you know how to get -1?

5. anonymous

use tanx=tany implies x=n(pi)+y where n is integer.

6. anonymous

u get cosa+sina=2n+1. when n=0 u get 1 and when n=-1 u get -1

7. anonymous

which means we can get any no. upto both ways of infinity??

8. anonymous

also use the fact that -rt(2)=<cosa+sina<=rt(2) which narrows down n to ONLY 0 and -1

9. anonymous

oh...okay..