Question

if tanQ =1/√7 then cosec²Q-sec²Q/cosec²Q+sec²Q is equal to (a) 5/7 (b)3/7 (c)1/12 (d) 3/4​

Answer 1

Answer:

option (d) . 3 / 4

Step-by-step explanation:

• so here we have tanQ = 1/ sqrt 7
• now cotQ will be = sqrt7
• so cotQ^2 = 7

now we know that (cosecQ^2 - cotQ^2) = 1

cosecQ^2= 1+7 (as cotQ^2 = 7)

cosecQ^2 = 8

now we also know that =(secQ^2 -tanQ^2)=1

so tanQ^2 = 1/ 7

so now= secQ^2 - tanQ^2 = 1

secQ^2 = 1+(1/7) = 8/7

so now lets put this value in our equation

cosecQ^2 - secQ^2/ cosecQ^2+ secQ^2

= 8 - (8/7)/ 8+ (8/7)

(48 /7)÷ (64/7) = (48/64)= (3/4)

Answer 2

Answer:

6/7 is correct answer

Step-by-step explanation:

cosecQ-ec²Q/cosec²Q+sec²Q

given tanQ =1/√7

solve it

(1/sin^2Q - 1/cos^2Q) / (1/sin^2Q + 1/cos^2Q)

taking LCM

(cos^2Q - sin^2Q /sin^2Qcos^2Q ) / ( cos^2Q + sin^2Q /sin^2Qcos^2Q )

denominator sin^2Qcos^2Q is cancel out

(cos^2Q - sin^2Q )/ (cos^2Q + sin^2Q)

by trigonometric formula (cos^2Q + sin^2Q)= 1

(cos^2Q - sin^2Q )/ 1

whole fraction is divided by cos^2Q

(1 - tan^2Q)

put tanQ =1/√7

1 - (1/√7)^2

1 - 1/7

(7-1)/7

6/7