Question

evaluate with out using trigonometric tables tan 20 degree x tan40 degree tan 50 tan 70​

Answer 1

Answer

Hiii !!

tan 20 x tan 40 x tan 50 x tan 70

so we use trigonometric ratio of complementary angles

remember , tan ( 90 - x ) = cot x

so we apply this here

tan 20 = tan (90 -70)  ......... 90-70=20

tan 50 = tan ( 90-40)  ............ 90-40=50

so, tan ( 90-70) = cot 70

    tan (90-40) = cot 40

then we get

              cot 70 x tan 70 x cot 40 x tan 40

                     1 x 1                                                .... ( cot theta x tan theta = 1 )

              = 1

hope it helps you !!!

:)

Answer 2

Answer:

1

Step-by-step explanation:

if your question is tan 20° * tan 40° * tan 50° * tan 70°

then,

tan 20° * tan 40° * tan 50° * tan 70°

(taking complementary function)

= cot(90° - 20°) * cot(90° - 40°) * tan 50° * tan 70°

= cot 70° * cot 50° * tan 50° * tan 70°

(rearranging)

= cot 70° * tan 70° * cot 50° * tan 50°

(applying reciprocal relation)

= 1 * 1

= 1