Question

sin(tan⁻¹(tan7π/6))+cos(cos⁻¹(cos7π/3)=.......,Select Proper option from the given options.
(a) -1
(b) 0
(c) 1
(d) √3/2

Answer 1

we have to find the value of sin[tan^-1(tan7π/6)]+cos[cos^-1(cos7π/3)]

we know, tan^-1(tanx) = x for , -π/2 < x < π/2

so, tan^-1(tan7π/6) = tan^-1[tan(π + π/6)]

= tan^-1[tan(π/6)] [ as we know, tan(π + x) = tanx]

= tan^-1(tanπ/6) = π/6

hence, tan^-1(tan7π/6) = π/6 .....(1)

again, cos^-1(cosx) = x , for -π/2 ≤ x ≤ π/2

so, cos^-1(cos7π/3) = cos^-1[cos(2π+π/3)]

= cos^-1[cos(π/3)] [as we know, cos(2π + x) = cosx]

= π/3

hence, cos^-1(cos7π/6) = π/3 ........(2)

now, from equations (1) and (2),

= sin[π/6 + π/3]

= sinπ/2

= 1

therefore option (c) is correct

Answer 2

HELLO DEAR,


sin[tan-¹(tan7π/6)] + cos[cos-¹(cos7π/3)]


we know:- tan-¹ (tanx) = x

so,
sin(7π/6) + cos(7π/3)

AND sin(π + x) = sinx and cos(2π + x) = cosx


therefore, sin(π + π/6) + cos(2π + π/3)

sinπ/6 + cosπ/3

(1/2) + (1/2)

(1 + 1)/2

2/2

1


hence, option (c) is correct.


I HOPE ITS HELP YOU DEAR,
THANKS