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