If 3π4<α<π then, √2cotα+1sin2α is equal to
1−cotα
1+cotα
−1+cotα
−1−cotα
We have:
=√2cotα+1sin2α
=√2cosαsinα+1sin2α
=√2sinαcosα+sin2α+cos2αsin2α
=√(sinα+cosα)2sin2α
=√(1+cotα)2
=|1+cotα|
=−(1+cotα)[When3π4<α<π,cotα<−1⇒cotα+1<0]
=−1−cotα
If cos A=45 and cos B=1213,3π2<A,B<2π, find the value of the following
(i) cos(A+b)
(ii) sin(A−B)