tan9-tan27-tan63+tan81=?
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Answered by
3
Step-by-step explanation:
subsititute tan81 = cot9 and tan63=cot27
By simplifying this you’ll get
tan^2(9) + 1/ tan9 - tan^2(27) +1/ tan27
tan^3(x)+1 = sec^2(x)
siimplify using this and you get
2/sin18 - 2/sin54
this gives you 2*( sin54 - sin18 / sin54sin18 )
= 2 * (2cos36sin18/sin54sin18) { using sinA - sinB = 2 cos(A+B/2)sin(A-B/2) }
= 4 ( cos36sin18/sin54sin18)
= 4
because cos36 = sin54 as 54 and 36 are complementary angles
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