`{:(,"स्तम्भ 'अ'",,,"स्तम्भ 'ब'"),((i),sin 765^(@)"का मान",(2019),(a),2-sqrt(3)),((ii),"tan"(13pi)/(12)"का मान",(2019),(b),-sin x),((iii),sin (2pi-x)"का मान",(2019),(c ),(1)/(sqrt(2))),((iv),sin 15^(@)"का मान",(2019),(d),cos x),((v),cos(2pi-x)"का मान",(2019),(e ),(sqrt(3)-1)/(2sqrt(2))):}`

Prove that (i) "sin " (7pi)/(12) " cos " (pi)/(2) - "cos " *(7pi)/(12) " sin " (pi)/(4) = (sqrt(3))/(2) (ii) " sin " (pi)/(4) " cos " (pi)/(2) + "cos"(pi)/(4) " sin " (pi)/(12) = (sqrt(3))/(2) (iii) " cos " (2pi)/(3) " cos " (pi)/(4) - " sin " (2pi)/(3) " sin " (pi)/(4) =(-(sqrt(3) +1))/(2sqrt(2))

f (x) = cos ((pi) / (sqrt (3)) sin x + sqrt ((2) / (3)) pi cos x)

" (8) "int(sin^(2)x-cos^(2)x)/(sin^(2)x cos^(2)x)dx" का मान ज्ञात कीजिए। "

यदि x+(1)/(x)=sqrt(3) है तब x^(3)+(1)/(x^(3)) का मान होगा -

Let g(x)=sqrt(sin^(-1)(cos(tan^(-1)x))+cos^(-1)(sin(cot^(-1)x))) ,then int_(-sqrt((pi)/(2)))^(sqrt((pi)/(2)))g(x)dx equals

Prove that (i) "cos " ((pi)/(3) +x) =(1)/(2) ( " cos " x - sqrt(3) sin x) (ii) " sin " ((pi)/(4) + x) + " sin " ((pi)/(4)-x) =sqrt(2) " cos " x (iii) (1)/(sqrt(2)) " cos ((pi)/(4) + x) = (1)/(2) " (cos x - sin x) " (iv) " cos x + cos " ((2pi)/(3) +x) + " cos " ((2pi)/(3)-x) =0

lim_(x rarr1^(-))(sqrt(pi)-sqrt(2sin^(-1)x))/(sqrt(1-x))=(A)sqrt((2)/(pi))(B)sqrt((pi)/(2))(C)(1)/(pi)(D)sqrt((1)/(pi))

" (a) "int_(0)^( pi/6)sqrt(1-sin2x)dx" का मान ज्ञात कीजिए "

The value of ("sin"(2019pi)/2-cos2019pi)/("tan"(2020pi)/3) is