Evaluate the following expressions :
(i) sin 
(ii) tan 
(iii) cosec 
(iv) tan 
(v) sin 
(vi) cos 
(vii) sec 
(viii) cos tan – 1 sin cot –1 
(ix) tan 
Text Solution
Verified by Experts(i) (ii); (iii) (iv); (v) (vi); (viii) (ix)
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 2 (viii) 
(ix) 
Sol. (i)sin cos–1 
= sin 
= 
(ii) tan 
= tan(tan–1 
) = 2 
(iii)cosec 
= cossec cosec–1 
= 
(iv)tan 
= tan tan–1 
= 
(v)sin= 
= sin 
cos cos–1 
+ cos 
sin cos–1 
= 
× 
+ 
= 
(vi)cos 
= cos sin–1 
cos cos–1 
– sin sin–1 
sin cos–1 
= 
= 
(vii)sec 
= sec tan tan–1 
= sec 
= 2
(viii)cos tan–1 
= cos cos–1 
= 
(ix)tan 
= cot sec–1 3 = cot cot–1 
= 
= 
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