Question

Prove it:cot A-tan A=2 cos²A-1/sin A cos A

Answer 1

CotA- tanA

=cosA/sinA- sinA/cosA

=cos^2A-sin^2A)/sinAcosA

=cos^2A-(1-cos^2A)/sinAcosA

=cos^2A-1+cos^2A/sinAcosA

=2cos^2A-1/sinAcosA

Answer 2

Answer:

$cotA-tanA =\frac{2cos^{2}A-1}{sinAcosA}$

Step-by-step explanation:

$LHS = cotA-tanA$

=$\frac{cosA}{sinA}-\frac{sinA}{cosA}$

= $\frac{cos^{2}A-sin^{2}A}{sinAcosA}$

=$\frac{cos^{2}A-(1-cos^{2}A)}{sinAcosA}$

= $\frac{cos^{2}A-1+cos^{2}A}{sinAcosA}$

=$\frac{2cos^{2}A-1}{sinAcosA}$

=$RHS$

Therefore,

$cotA-tanA =\frac{2cos^{2}A-1}{sinAcosA}$

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