Prove that $\frac{\sec \mathrm{A}-1}{\sec \mathrm{A}+1}=\frac{1-\cos \mathrm{A}}{1+\cos \mathrm{A}}$.

Important Questions on Trigonometrical Identities

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 21 - Trigonometrical Identities>EXERCISE>Q 2

Prove that$\frac{1+\sin \mathrm{A}}{1-\sin \mathrm{A}}=\frac{\cos {\displaystyle \mathrm{ec}}{\displaystyle }{\displaystyle \mathrm{A}}{\displaystyle +}{\displaystyle 1}}{\cos {\displaystyle \mathrm{ec}}{\displaystyle }{\displaystyle \mathrm{A}}{\displaystyle -}{\displaystyle 1}}$.

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 21 - Trigonometrical Identities>EXERCISE>Q 3

Prove that $\frac{1}{\tan \mathrm{A}+\cot \mathrm{A}}=\cos \mathrm{A} \sin \mathrm{A}$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 21 - Trigonometrical Identities>EXERCISE>Q 4

Prove that $\tan \mathrm{A}-\cot \mathrm{A}=\frac{1-2 {\cos }^2 \mathrm{A}}{\sin \mathrm{A} \cos \mathrm{A}}$.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 21 - Trigonometrical Identities>EXERCISE>Q 5

Prove that ${\sin }^4 \mathrm{A}-{\cos }^4 \mathrm{A}=2 {\sin }^2 \mathrm{A}-1$.

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 21 - Trigonometrical Identities>EXERCISE>Q 6

Prove that $(1-\tan \mathrm{A}{)}^2+(1+\tan \mathrm{A}{)}^2=2{\sec }^2 \mathrm{A}$.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 21 - Trigonometrical Identities>EXERCISE>Q 7

Prove that ${\mathrm{cosec}}^4 \mathrm{A}-{\mathrm{cosec}}^2 \mathrm{A}={\cot }^4 \mathrm{A}+{\cot }^2 \mathrm{A}$.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 21 - Trigonometrical Identities>EXERCISE>Q 8

Prove that $\sec \mathrm{A} (1 - \sin \mathrm{A}) (\sec \mathrm{A} + \tan \mathrm{A})= 1$.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 21 - Trigonometrical Identities>EXERCISE>Q 9

Prove that$\mathrm{cosec} \mathrm{A} (1 + \cos \mathrm{A}) (\mathrm{cosec} \mathrm{A} - \cot \mathrm{A})= 1$.