Show that `1-2sinthetacosthetage0`for all `theta in R`

Show that tan^2theta+cot^2thetage2 for all theta in R

Which of the following sentenced are statements in logic ? Justify. Write down the truth values of the statements : cos^2theta-sin^2theta = cos^2theta for all theta in R .

Let f : (-1, 1) -> R be such that f(cos4theta) = 2/(2-sec^2theta for theta in (0, pi/4) uu (pi/4, pi/2) . Then the value(s) of f(1/3) is/are

Show that: (frac(sin3theta+2sin5theta+sin7theta)(sintheta+2sin3theta+sin5theta))=cos2theta+sin2thetacot3theta

If "cosec " theta - sin theta = m, sec theta - cos theta =n , " then "(m^(2)n)^(2//3) + (mn^(2))^(2//3) =.................. A) 1 B) 2 C) 1/2 D) 0

If sqrt3 tan theta = 3 sin theta , find the value of sin theta^2 theta - cos^2 theta , where theta ne 0 .

2cos^2theta-2sin^2theta=1 then theta =

If x= a(cos theta + sin theta ), y= a(sin theta + cos theta ), then [( d^2 y)/(d x^2 ) ] at theta = pi /4 ............. A) 0 B) 1 C) -1 D) 1/sqrt 2

If theta lies in the first quadrant and 5 tan theta = 4 , " then " (5 sin theta - 3 cos theta )/( sin theta + 2 cos theta )= .............. A) 0 B) 1 C) 1/6 D) 5/14