Question

without using trigonometric tables prove that : tan 1 tan 11 tan 21 tan 69 tan79 tan89 = 1
plz solve it plz

Answer 1

Answer:

LHS=tan 1 tan 11 tan 21 tan 69 tan79 tan89

we have to find any two angle whose sum is 90

tan 1 tan 89 tan 21 tan 69 tan11 tan79

tan1 tan(90-1) tan21 tan(90-21) tan11 tan(90-11)

tan 1 cot1 tan11 cot11 tan 21 cot21 = 1

we know that tan×cot =1 always

1×1×1×1=1

LHS=RHS