Question

trigonometric ratio of complementary angle

Evaluate.

1•) tan 50° + sec 50°/cot 40°+codec 40 + cos 40°•cosec50°

​

Answer 1

Step-by-step explanation:

Value of Sec50°sin40°+cos40°cosec50° = 2

Step-by-step explanation:

Value of sec50°sin40°+cos40°cosec50°

= sec(90°-40°)sin40°+cos40°cosec(90°-50°)

= cosec40°sin40°+cos40°sec40°

/* Since ,

i)sec(90°-A) = cosecA

ii) cosec(90°-A)=secA

*/

= \frac{1}{sin40}\times sin40 + cos40 \times \frac{1}{cos40}

sin40

1

×sin40+cos40×

cos40

1

After cancellation, we get

= 1+11+1

= 22

Therefore,

Value of Sec50°sin40°+cos40°cosec50° = 2