1.

If `cos25^0+sin25^0=p ,`then `cos50^0`is(a)`sqrt(2-p^2)`(b) `-sqrt(2-p^2)`(c)`psqrt(2-p^2)`(d) `-psqrt(2-p^2)`

Answer» `cos25^@+sin25^@ = p`
Squaring both sides,
`=>cos^2 25^@+sin^2 25^@+2sin25^@cos25^@ = p^2`
`=>1+sin 50^@ = p^2`
`=>sin50^@ = p^2-1`
`=>cos50^@ = sqrt(1-sin^2 50^@)`
`=sqrt(1-(p^4+1-2p^2))`
`=psqrt(2-p^2)`
`:. cos50^@ = psqrt(2-p^2)`
So, option `c` is the correct option.


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