State true or false-cosec A-sin A A-cos Atan A- A-2

The correct option is B False (cosecA sinA)(secA cosA)(tanA+cotA) = (1/sinA sinA)(1/cosA cosA)(sinA/cosA+cosA/sinA) = (1 sin^2A/sinA)(1 cos^2A/cosA)(sin^2A+cos ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Identities

State true or...

Question

State true or false:

$(c o s e c A - s i n A) (s e c A - c o s A) (t a n A + c o t A)$ = 2

True

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False

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Solution

The correct option is B
False

$(c o s e c A - s i n A) (s e c A - c o s A) (t a n A + c o t A)$

= $(\frac{1}{s i n A} - s i n A) (\frac{1}{c o s A} - c o s A) (\frac{s i n A}{c o s A} + \frac{c o s A}{s i n A})$

= $(\frac{1 - s i n^{2} A}{s i n A}) (\frac{1 - c o s^{2} A}{c o s A}) (\frac{s i n^{2} A + c o s^{2} A}{s i n A c o s A})$

= $(\frac{c o s^{2} A}{s i n A}) (\frac{s i n^{2} A}{c o s A}) (\frac{1}{s i n A c o s A})$

= 1

Suggest Corrections

State true or false: (cosecA−sinA)(secA−cosA)(tanA+cotA) = 2

The correct option is B False (cosecA−sinA)(secA−cosA)(tanA+cotA) = (1sinA−sinA)(1cosA−cosA)(sinAcosA+cosAsinA) = (1−sin2AsinA)(1−cos2AcosA)(sin2A+cos2AsinAcosA) = (cos2AsinA)(sin2AcosA)(1sinAcosA) = 1

State true or false:

$(c o s e c A - s i n A) (s e c A - c o s A) (t a n A + c o t A)$ = 2