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Some trig questions

Hello i have some trig questions:

For the following function, determine the max and min value of 'y' and the least positive value of'x' at which these occur.

y= 60 / (1 + sin²(2x-15) )

Solve the following equation for theta, giving solutions in the interval 0 <=(theta)<=360

2-2cos²(theta) = sin (theta)

tan²(theta) - 2tan(theta) = 1

Thanks a lot
From John

Reply 1

Chewwy

1) i'd just do it by inspection. reciprocal of sin^2 u will be min when sin^2 u is max, and the converse.

since -1<=sinu<=1, 0<=sin^2 u < 1, with the min and max values occuring at (kpi) and (kpi+pi/2) respectively. plug these in to find y...

2) remember cos^2 x = 1-sin^2 x. replace, and solve the quadratic.

3) bring the 1 across to the LHS, call substitute u for tax x for u if it makes things easier, solve the quadratic for this u.