Question

The value of
tan 57° - tan 12º – tan 57° tan 12° is
76)(A) tan 69° (B) tan 45º
(C) 0
(D) tan 57°​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The value of tan 57° - tan 12º – tan 57° tan 12° is

(A) tan 69°

(B) tan 45º

(C) 0

(D) tan 57°

EVALUATION

$\displaystyle \sf{ \tan {45}^{ \circ} = 1}$

$\displaystyle \sf{ \implies \: \tan ({57}^{ \circ} - {12}^{ \circ} ) = 1}$

$\displaystyle \sf{ \implies \: \frac{\tan {57}^{ \circ} -\tan {12}^{ \circ} }{1 + \tan {57}^{ \circ} \tan {12}^{ \circ} } = 1}$

$\displaystyle \sf{ \implies \: \tan {57}^{ \circ} -\tan {12}^{ \circ} = 1 + \tan {57}^{ \circ} \tan {12}^{ \circ} }$

$\displaystyle \sf{ \implies \: \tan {57}^{ \circ} -\tan {12}^{ \circ} - \tan {57}^{ \circ} \tan {12}^{ \circ} = 1 }$

$\displaystyle \sf{ \implies \: \tan {57}^{ \circ} -\tan {12}^{ \circ} - \tan {57}^{ \circ} \tan {12}^{ \circ} = \tan {45}^{ \circ} }$

FINAL ANSWER

Hence the correct option is (B) tan 45º

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Answer 2

Answer:

Step-by-step explanation:

B) tan 45