If sin A sin B- cos A cos B - 1- 0- then the value of 1- A tan B is

Given, sin A sin B cos Acos B+1= 0 ⇒cos A cos B nbsp;sin A sin B =1 ⇒cos (A+B) =1 ⇒sin (A+B) = √(1 cos^2 (A+B)) = 0 ⇒sin Acos B+sin Bcos A = 0 ⇒ nbsp;sin ...

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Standard XIII

Mathematics

Tangent, Cotangent, Secant, Cosecant in Terms of Sine and Cosine

If sin A sin ...

Question

If $sin A sin B - cos A cos B + 1 = 0$ , then the value of $1 - cot A tan B$ is

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Solution

Given,
$sin A sin B - cos A cos B + 1 = 0 \Rightarrow cos A cos B - sin A sin B = 1 \Rightarrow cos (A + B) = 1 \Rightarrow sin (A + B) = \sqrt{1 - {cos}^{2} (A + B)} = 0 \Rightarrow sin A cos B + sin B cos A = 0 \Rightarrow sin A cos B = - sin B cos A \Rightarrow 1 = - cot A tan B ∴ 1 - cot A tan B = 2$

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If sinAsinB−cosAcosB+1=0, then the value of 1−cotAtanB is

Given, sinAsinB−cosAcosB+1=0⇒cosAcosB−sinAsinB=1⇒cos(A+B)=1⇒sin(A+B)=√1−cos2(A+B)=0⇒sinAcosB+sinBcosA=0⇒sinAcosB=−sinBcosA⇒1=−cotAtanB∴1−cotAtanB=2

If $sin A sin B - cos A cos B + 1 = 0$ , then the value of $1 - cot A tan B$ is