Question

log (sec²x-tan²x) to the base cot221/2degree​

Answer 1

Answer:Tan (A/2) =Sin (A/2) / Cos (A/2)

Multiply and divide by 2 Cos (A/2)

Tan (A/2) = {2 Cos (A/2) Sin (A/2) } / { 2 Cos (A/2) Cos (A/2)}………….(1)

Sin A=2Sin(A/2) Cos(A/2) …..(2);

Cos A= Cos^2 (A/2)- Sin^2 (A/2)=2 Cos^(A/2) - 1

Cos A + 1=2 Cos^(A/2) …..(3);

==> Tan (A/2) = Sin A/(Cos A + 1) ……(comparing 1 with 2 & 3)

==>Cot (A/2) = (Cos A + 1) / Sin A

==> Cot(22.5) = (Cos 45 + 1) / Sin 45

==> Cot(22.5) = ((1 / √2 ) + 1)/ (1 / √2 ) = √2 + 1

Step-by-step explanation: