.~ 2(3.J3 +2J2.)

- ____ ___.._ - ----

2 I

= 3.fj + 2 J2. Ans. Q. 13. Sho\v that 4 (sin4 30 + cos4 G0)

- 3 (cos2 45 - sin2 90) = 2. Sol. L.H.S. = 4 (sin4 30 + cos4 G0)

- 3 ( cos2 45 - sin2 90)

-3 (~r-(1)2 = 4 [-1 + __!_]- 3 [..!.. - I J 16 1 G 2 = 4 x 1

26 - 3 x ( - ~ )

=_!_+I=.:!.= 2 = R. H.S. 2 2 2

Q. 14. Without using tables, verify that : (i) cos 60 = (cos2 30 - sin2 30).

(ii) sin 600 = 2 tan 300 = .J3. I+ tan2 30 2

(iii) cos 600 = l - tan 2 3 00 - _!_. I+ tan2 30 2

1 Sol. (i) L. H. S. =cos 60 = 2" R.H.S. = cos2 30 - sin2 30

:. L.H.S. = R.H.S.

(ii) sin 60 = .fj 2

I 2x-2 tan 3 0 .J3

and -----1 + tan 2 30" I + ( )Jr

2 2 .J3 .J3

- -I 1 +- 4 3 3

2 3 3 3.fj --x-- ------ .J3 4 - 2.J3 - 2 x .J3 x J3

3J3 J3 -----

2x3 2 Hence proved.

1 (iii) L. H. S. = cos 60 = -2

1- tan2 30 1-(i=J2 and -

I + tan 2 3 0 ( ) 2 I+ ~

1 2 1 - -__ 3 3 2 3 1

- I =-=-x-=-1+ - 4 3 4 2

3 3 Hence proved.

Q. 15. If0 tan x0 = 1 = tan 45 .

. . x0

= 45 .

. . x = 45 Ans . EXEiCISE 22 fC)

Q. 1. Without using trigono1netric tables. evaluate the follo\ving :

sin 10 (i) cos 80

tan 25 (iii) t 6 0 co )

COS 12 (ii) . 780 .

Sill