Question

D cos ( 2 x=2 cos ^{2} x-1 )
" ( cos u x+cos ^{2} x=3 cos ^{2} x-1 )
( 0 leq cos ^{2} x leq 1 )
( 0 leq 3 cos ^{2} x leq 3 )
( -1 leq 3 cos ^{2} x-1 leq 2 )
( - )
( therefore cos 2 x+cos ^{2} x inleft[begin{array}{cc}-1 & 2end{array}right] )
11) ( quadleft[cos left(x+frac{pi}{4}right)right]^{2}=left(frac{cos x}{sqrt{2}}-frac{sin x}{sqrt{2}}right)^{2} )
( begin{aligned} &=frac{(cos x-sin x)^{2}}{2} therefore quad cos ^{2}(pi / u+x)+(sin x-cos x)^{2} =& frac{3}{2}(cos x-sin x)^{2} therefore &(cos x-sin x)^{2} in[0,2] therefore & frac{3}{2}[cos x-sin x)^{2} in[0,3] end{aligned} )

# Find the maximum and minimum values of following trigonometric functions E-2. Find the cos 2x + cos2x (ii) cosa (+ x + (sinx – cos x)2

Solution