sec θ cosec(900-9)-tan θ cot(900-9) + (sin, 350 + sin2 550)tan 10 ta

1.	sec θ cosec(900-9)-tan θ cot(900-9) + (sin, 350 + sin2 550)tan 10 tan 20 tan 450 tan 70° tan 806. Evaluate without using tables:OR
Answer» Let theta = xThen,secx. cosec(90-x) - tanx. cot(90-x) + (sin^2 35 + sin^2 55)/(tan10. tan20. tan45. tan70.tan 80) = secx. secx - tanx. tanx + (sin^2 35 + cos^2 (90 - 55))/(cot(90-10).cot(90-20). tan45.tan70.tan80 = (sec^2 x - tan^2 x) + (sin^2 35 + cos^2 35)/cot80.cot70.tan45.tan70.tan80 = 1 + 1/11tan45 = 2/1 = 2

sec θ cosec(900-9)-tan θ cot(900-9) + (sin, 350 + sin2 550)tan 10 tan 20 tan 450 tan 70° tan 806. Evaluate without using tables:OR

Answer»

Let theta = xThen,secx. cosec(90-x) - tanx. cot(90-x) + (sin^2 35 + sin^2 55)/(tan10. tan20. tan45. tan70.tan 80)

= secx. secx - tanx. tanx + (sin^2 35 + cos^2 (90 - 55))/(cot(90-10).cot(90-20). tan45.tan70.tan80

= (sec^2 x - tan^2 x) + (sin^2 35 + cos^2 35)/cot80.cot70.tan45.tan70.tan80

= 1 + 1/1*1*tan45

= 2/1

= 2