Question

evaluate cos 65 degree upon sin 25 degree minus tan 20 degree upon cot 70 degree minus sin 90 degree + tan 5 degree tan 35 degree tan 60 degree tan 55 degree tan 85 degree​

Answer 1

Correct Order: cos65°/sin25° - tan20°/cot70° - sin90° + tan5° tan35° tan60° tan55° tan85°

Solution: Remember these identities -

• cos∅ = sin(90° - ∅)
• tan∅ = cot (90° - ∅)
• sin90° = 1
• tan60° = √3
• tan∅ cot∅ = 1

→ sin(90° - 65°)/sin25° - cot(90° - 20°)/cot70° - 1 + cot(90° - 5°) cot(90° - 35°) × √3 × tan55° tan85°

→ sin25°/sin25° - cot70°/cot70° - 1 + cot85° cot55° × √3 × tan55° tan85°

→ 1 - 1 - 1 + √3

→ √3 - 1

Answer is √3 - 1

Answer 2

Answer:

$\displaystyle{\rightarrow \sqrt{3}-1}$

Step-by-step explanation:

Given :

$\displaystyle{\frac{\cos65}{\sin25} -\frac{\tan20}{\cot70}-\sin90+\tan5.\tan35.\tan60.\tan55.\tan85}$

Using complementary formula :

$\displaystyle{\frac{\cos65}{\cos65} -\frac{\tan20}{\tan20}-\sin90+\tan5.\tan35.\tan60.\cot35.\cot5}$

$\displaystyle{1-1-\sin90+1/\cot5./1\cot35.\tan60.\cot35.\cot5}$

$\displaystyle{-\sin90+\tan60}$

We know the value of :

sin 90 = 1

tan 60 = √ 3

$\displaystyle{\tan60-\sin90}\\\\\\\displaystyle{\rightarrow \sqrt{3}-1}$

Hence we get answer.