If $$ {Acos^{2}θ+Bsin^{2}θ}={sin^{2}θ(sec^{2}θ+1)\over{sec^{2}θ-1}}$$ and cotθ=?

If a cot θ + b cosec θ= p and b cot θ + a cosec θ = q then p² -q² is equal to _____

Which of the following values suits for A to make the equation  $$ {{ATan62°Sec 28°Cot 38°}\over {Cosec62°Tan11°}}=1$$ ?

If sin²a = cos³a then the value of cot⁶ a – cot²a? 

If 5sinθ – 4cosθ=0, 0°˂θ˂90°, then the value of $$ {5\sinθ-2\cosθ}\over {5\sinθ+3\cosθ}$$ is:

If $$ {tan\ θ={a\over b}}$$ then $$ {a\sinθ+b\cosθ\over{a\sinθ-b\cosθ}}$$  is

$$(1+tan θ+secθ)(1+cotθ-cosecθ)\over (sec θ+tan θ)(1-sin θ) $$ is equal to :

Evaluate the following.

sin 25° sin 65° – cos 25° cos 65°.