Question

Hey !!

TRIGONOMETRIC RATIOS :


Show that :

1-tan² A / cot² A - 1 = tan² A


No Copied Answers !!​

Answer 1

To Prove

→ (1 - tan²A)/(cot²A - 1) = tan²A

L.H.S → (1 - tan²A)/(cot²A - 1)

Since we know that,

• cot ∅ = 1/tan∅

Denominator → (1/tanA)² - 1

→ 1/tan²A - 1

→ (1 - tan²A)/tan²A

Numerator/Denominator

→ (1 - tan²A)/(1 - tan²A)/tan²A

→ tan²A = R.H.S

Hence L.H.S and R.H.S are equal

Hence Proved

Answer 2

# Heya Mate #

Here is your answer

_____________________________

Identities ( used in answer) :-

(i) Cosec^2A - Cot^2A = 1

(ii) Sec^2A - Tan^2A =1

(iii) Sec^2A = 1/Cos^2A

(iv) Cosec^2A = 1/Sin^2A

(v) Sin^2A/Cos^2A= Tan^2A

Now,

Proof:-

1-Tan^2A/Cot^2A-1

= - Sec^2A / - Cosec^2A

[ Using identities (i) and (ii)]

= Sec^2A/Cosec^2A

(Minus sign was removed because it was in both denomination as well as in numerator)

Now put value of Sec^2A and Cosec

[By using identities (iii) and (iv)]

= 1/Cos^2A/1/Sin^2A

= 1/Cos^2A * Sin^2A/1

So,

= Sin^2/Cos^2A

= Tan^2A

[ By identity (v) ]

Hence Proved

______________________

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