Question

Prove that trigonometric identity : (sec²A-1)cot²A=1​

Answer 1

Step-by-step explanation:

sec²A - 1 = tan²A [ tan²A + 1 = sec²A ]

therefore LHS => (sec²A - 1)cot²A = tan²A * cot²A

=> tan²A * 1/tan²A [ cot A = 1/tan A ]

=> 1 = RHS

hence proved

Answer 2

To prove:

(sec²A - 1) cot²A = 1

Identities used:

• tan²A = sec²A - 1
• cot²A = 1 ÷ tan²A

Proof:

(sec²A - 1) can also be written as tan²A.

(sec²A - 1) cot²A

→ (tan²A) cot²A

cot²A can be written as 1/tan²A

→ tan²A × 1/tan²A

Cancelling tan²A in numerator and denominator, we get 1.

So (sec²A - 1) cot²A = 1

★ HENCE PROVED ★

Know more:

$\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ \: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1 \end{minipage}}$