1.

The maximum value of `1+sin(pi/4+theta)+2cos(pi/4-theta)` for real values of `theta` isA. 3B. 5C. 4D. none of these

Answer» Correct Answer - C
We have,
`y=1+sin ((pi)/(4)+theta)+2cos((pi)/(4)-theta)`
`impliesy=1+(1)/(sqrt2)(sin theta+costheta)+sqrt2(cos theta+sin theta)`
`impliesy=1+(sqrt2+(1)/(sqrt2))sintheta+(sqrt2+(1)/(sqrt2))costheta [becausecostheta+sinthetalesqrt2]`
`impliesy=1+(sqrt2+(1)/(sqrt2))(cos theta+sintheta)`
`impliesyle1(sqrt2+(1)/(sqrt2))sqrt2impliesyle4`
Hence, the maximum value is 4,


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