Question

Evaluate the following: `(2sin25° sin35° sec55° sec65°)/(5tan 29° tan45° tan61°) + (3cos20° cos50° cot70° cot40°)/(5tan20° tan50° sin70° sin40°)`

Answer 1

`(2sin25° sin35° sec55° sec65°)/(5tan 29° tan45° tan61°) + (3cos20° cos50° cot70° cot40°)/(5tan20° tan50° sin70° sin40°)`

= `(2sin(90° - 65°) sin(90° - 55°) sec55° sec65°)/(5tan(90° - 61°) xx 1 xx tan61°)`

= `(3cos(90° - 70°) cos(90° - 40°) cot(90° - 20°) cot(90° - 50°))/(5tan20° tan50° sin70° sin40°)`

= `(2cos65° cos55° xx 1/(cos55°) xx 1/(sec65°))/(5cot61° xx 1 xx 1/(cot61°)) + (3sin70° sin40° tan20° tan50°)/(5tan20° tan50° sin70° sin40°)`

= `(2)/(5) + (3)/(5)`

= `(5)/(5)`
= 1.