If A-B-90- then the value of tan 2 A- 2 B is

A+B=90 #176; #8658;A=90 #176; B #8658;tanA=tan90 #176; B #8658;tanA=cotB #160; #160; #160; #160; #160; #160; #160; #160; #160; ...

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Standard XII

Mathematics

Trigonometric Ratios of Compound Angles

If A+B=90∘, t...

Question

If A + B = 90°, then the value of tan² A – cot² B is _________.

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Solution

$A + B = 90 ° \Rightarrow A = 90 ° - B \Rightarrow \tan A = \tan (90 ° - B) \Rightarrow \tan A = \cot B [\tan (90 ° - θ) = \cot θ]$
$∴ \tan^{2} A - \cot^{2} B = \cot^{2} B - \cot^{2} B = 0 (\tan A = \cot B)$

If A + B = 90°, then the value of tan² A – cot² B is 0.

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If A + B = 90°, then the value of tan2 A – cot2 B is _________.

A+B=90°⇒A=90°-B⇒tanA=tan90°-B⇒tanA=cotB tan90°-θ=cotθ ∴tan2A-cot2B=cot2B-cot2B=0 tanA=cotB If A + B = 90°, then the value of tan2 A – cot2 B is ____0____.

If A + B = 90°, then the value of tan² A – cot² B is _________.

$A + B = 90 ° \Rightarrow A = 90 ° - B \Rightarrow \tan A = \tan (90 ° - B) \Rightarrow \tan A = \cot B [\tan (90 ° - θ) = \cot θ]$
$∴ \tan^{2} A - \cot^{2} B = \cot^{2} B - \cot^{2} B = 0 (\tan A = \cot B)$

If A + B = 90°, then the value of tan² A – cot² B is 0.