Question

4x
27.
Without using trigonometric tables, evaluate
- tan
cot (90°- 0) + seco cosec (90°- 0)+sin? 35° + sin2 55°
tan 10° tan 20° tan 30° tan 70° tan 80°
28. Without using trigonometric tables, evaluate
80p2 100 - COR 30° + sin 15° cos 75° + cos 15° sin 75°
cos O sin (90°- 0)+sin cos (90°-0)​

Answer 1

Step-by-step explanation:

27.

Let theta = A, for simplicity in solution.

Numerator 

= Sec A cosec(90-A)  - Tan A Cot(90 - A) + sin² 55 + sin² 35

= Sec A * sec A - tan A * tan A + sin² 55 + Cos² (90-35)

= 1 + 1

= 2

as  sin²A + cos²A = 1  for any angle A.

sec²A - tan²A = 1   for any angle

cosec(90-A) = sec A

cot (90-A) = tan A

=====

we know  that    tan A = cot (90-A) = 1 / tan (90-A) .    Let us apply this.

Denominator

 = tan 10  tan 80  tan 60  tan 20 tan 70

 = tan 10 * 1/tan10  * tan 60 *  tan 20 * 1/tan20

 = tan 60

 = √3

Answer 2

Answer:

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