Question

tan15x° tan 75° x tan15° x tan 75° =
Explain Value

Answer 1

solution

tan15°= cot(90-75°) = cot 75°
tan75°= cot(90°-15°)= cot 15°

Now, (cot75°* tan75° ) (cot15°*tan15°)

= 1*1

= 1

__________

hope it helpz☺

Answer 2

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= tan 15°  * tan 75°  * tan 15°  * tan 75°

We can write tan 15° as tan ( 90° - 75° ).

= tan ( 90° - 75° ) * tan 75° * tan ( 90­° - 75° ) * tan 75°

We know that tan ( 90° - a ) = cot a

                            tan ( 90° - 75° ) = cot 75°.

Now,

= cot 75° * tan 75° * cot 75° * tan 75°

= cot 75° * ( 1 / cot 75° ) * cot 75° * ( 1 / cot 75° )  [ cot a = 1 / tan a ]

= 1.