निम्नलिखित को सिद्ध कीजिये
(i) `((1-cos B) (1+cos B))/((1-sin B) (1+sin B))=1/3" जब "B=30^@`
(ii) `((1-cos alpha) (1+cos alpha))/((1-sin alpha) (1+sin alpha))=3" जब "alpha=60^@`
(iii) `cos (A-B)=cos A. cos B+sin A. sin B" यदि "A=B=60^@`
(iv) `4(sin^4 30^@+cos^4 60^@)-3 (cos^2 45^@-sin^2 90^@)=2`
(v) `sin 90^@=2 sin 45^@. cos 45^@`
(vi) `cos 60^@=2 cos^2 30^@-1=1-2sin^2 30^@`
(vii) `cos 90^@=1-2 sin^2 45^@=2 cos^2 45^@-1`
(viii) `sin 30^@. cos 60^@+cos 30^@. sin60^@=sin 90^@`
(ix) `cos60^@.cos30^@-sin 60^@. sin30^@=cos 90^@`

Answer

(i) `1/3` (ii) 3 (iii) 1 (iv) 2 (v) 1 (vi) `1/2` (vii) 0 (viii) 1 (ix) 0 (x) `1/2`
(xi) `1/sqrt3` (xii) `2-sqrt3` (xiii) `sqrt3/2` (xiv) `sqrt3/2`