Question

If 0 ≤ x ≤ 2π , then find sin (x/2 ) , cos (x/2) and tan (x/2) if tan x = ( -4 /3 ) and x
lies in II quadrant.​

Answer 1

Step-by-step explanation:

Gaangi sec θ = √2 ⇒ cos θ = 12√12 ∴ sin θ = ±1−cos2θ−−−−−−−−√1−cos2θ = ±1−12−−−−−√1−12 = ±12√12 Since θ lies in the fourth quadrant, so sin θ is –ve and cos q is +ve. ∴ sin θ = −12√−12, cosec θ = √2 tan θ = sinθcosθsinθcosθ = −12√−12 x 2√121 = –1 ⇒ cot θ = –1 ∴ 1+tanθ+cosecθ1+cotθ−cosecθ1+tanθ+cosecθ1+cotθ−cosecθ = 1−1−2√1−1+2√=−1.Read more on Sarthaks.com - https://www.sarthaks.com/995221/if-sec-2-and-3-2-2-find-the-value-of

Answer 2

Step-by-step explanation:

option is

A

(a) (i)261(ii)133(iii)263(iv)521

B

(b) (i)41(ii)521(iii)136

C

(c) (i)1310(ii)131

In  52 cards getting a one card as 52 times 

a.(1) The king in card is two getting in 2 times 

Then  probability =522=261

(ii)In 52 cards the king ,queen and joker are three face card.Then total face cards are 12.So these card get 12 times 

Then probability =5212=133

(!!!)In 52 cards the  red face card  are 3 face card.Then total

red face cards are 3.So these card get 6 times

Then probability =526=263

(iv)In 52 cards the  jack of heart card is one .So the getting time card is one

Then probability =$$\frac{1}{52}

(b) (i)In 52 cards the  spade cards are 13. So getting time is 13

Then probability =5213=41

(ii)In 52 cards the queen of diamonds is one .So getting time is one

Then probevility=521

(iii)In 52 cards Neither a red card nor a queen the total cards are

24.So time of getting cards are 24

Then probability =52