7If two zeros of the polynomial х"-4X-stWithout using trigonometric t

1.	7If two zeros of the polynomial х"-4X-stWithout using trigonometric tables, find the value of the following expression:sec (90°-6) . cosec θ-tan (90°-6) cot θ + cos2 25° + cos2 65°3 tan 27° tan 63o
Answer» 1 )Sec ( 90 - A ) = cosecA 2 ) Tan( 90 - A ) = cot A 3 )Cos 25 = cos ( 90 - 65 ) = sin65 4 )Tan 27 = tan ( 90 - 63 ) = cot 63 5 ) cosec²A - cot² A = 1 6 ) sin² A + cos² A = 1 7 ) cotA tanA = 1 Now , Sec(90-A)cosecA - tan( 90-A)cotA+ cos² 25 + cos² 65/ 3tan27tan63 = CosecAcosecA - cotAcotA + sin²65+cos²65/3cot63tan63 =( Cosec² A - cot² A)+ ( sin²A+cos²A)/ 3cot63tan63 = ( 1 + 1 )/ 3 = 2/3

7If two zeros of the polynomial х"-4X-stWithout using trigonometric tables, find the value of the following expression:sec (90°-6) . cosec θ-tan (90°-6) cot θ + cos2 25° + cos2 65°3 tan 27° tan 63o

Answer»

1 )Sec ( 90 - A ) = cosecA

2 ) Tan( 90 - A ) = cot A

3 )Cos 25 = cos ( 90 - 65 ) = sin65

4 )Tan 27 = tan ( 90 - 63 ) = cot 63

5 ) cosec²A - cot² A = 1

6 ) sin² A + cos² A = 1

7 ) cotA tanA = 1

Now ,

Sec(90-A)cosecA - tan( 90-A)cotA+ cos² 25 + cos² 65/ 3tan27tan63

= CosecAcosecA - cotAcotA + sin²65+cos²65/3cot63tan63

=( Cosec² A - cot² A)+ ( sin²A+cos²A)/ 3cot63tan63

= ( 1 + 1 )/ 3

= 2/3