Mathematics

Problem

3. Choose the correct option. Justify your choice. (i)

9 \sec ^{2} \mathrm{~A}-9 \tan ^{2} \mathrm{~A}=

(A) 1 (B) 9 (C) 8 (D) 0 (ii)

(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)=

(A) 0 (B) 1 (C) 2 (D) -1 (iii)

(\sec \mathrm{A}+\tan \mathrm{A})(1-\sin \mathrm{A})=

(A)

\sec \mathrm{A}

(B)

\sin \mathrm{A}

(C)

\operatorname{cosec} \mathrm{A}

(D)

\cos \mathrm{A}

(iv)

\frac{1+\tan ^{2} \mathrm{~A}}{1+\cot ^{2} \mathrm{~A}}=

(A)

\sec ^{2} \mathrm{~A}

(B) -1 (C)

\cot ^{2} \mathrm{~A}

(D)

\tan ^{2} \mathrm{~A}