What is the maximum value of `1/(cos ec \ theta)`?

Express 2cos theta + 3 sin theta in the form r cos ( theta - alpha ), where r is positive, stating the values of r and alpha. What is the maximum value of 2 cos theta + 3 sin theta ?

A cube of side a is placed on an inclined plane of inclination theta . What is the maximum value of theta for which the cube will not topple?

What is the minimum value of (sin^2theta+cos^4theta) ?

What is the value of (1-cos^2theta)cos e c^2theta ?

veca, vecb and vecc are unit vecrtors such that |veca + vecb+ 3vecc|=4 Angle between veca and vecb is theta_(1) , between vecb and vecc is theta_(2) and between veca and vecb varies [pi//6, 2pi//3] . Then the maximum value of cos theta_(1)+3cos theta_(2) is

veca, vecb and vecc are unit vecrtors such that |veca + vecb+ 3vecc|=4 Angle between veca and vecb is theta_(1) , between vecb and vecc is theta_(2) and between veca and vecb varies [pi//6, 2pi//3] . Then the maximum value of cos theta_(1)+3cos theta_(2) is

What is the value of 6tan^2theta-6/(cos^2theta) ?

In the figure above, IF cos theta =3/5 , what is the value of cos (90-theta) ?

Statement I The maximum value of sin theta+costheta is 2. Statement II The maximum value of sin theta is 1 and that of cos theta is also 1.

For theta in(0,pi/2) , the maximum value of sin(theta+pi/6)+cos(theta+pi/6) is attained at theta =