# The Value of (cosec a- sin a)(sec a – cos a)(tan a + cot a) :

**Answer is (4): 1**

**Explanation:-**(cosec a – sin a) (sec a – cos a)(tan a+ cot a)

= (1/sin a – sin a) (1/cos a – cos a) (tan a + 1/tan a)

= {(1 – sin

^{2}a)/sin a}{(1 – cos

^{2}a)/cos a}{(1 + tan

^{2}a)/tan a}

= (cos

^{2}a/sin a) (sin

^{2}a/cos a) (sec

^{2}a/tan a)

= cos a sin a (cos a/sin a x cos

^{2}a)

= sin a cos a/sin a cos a

= 1

Hence, the answer is (4) 1.