f79d99da448054afdbd953059fe5db14
2021.43
testbook.com
f79d99da448054afdbd953059fe5db14
"710 + 710 + 710 + 710 + 710 + 710 + 710  = 7n"
"710 + 710 + 710 + 710 +&n"
testbook.com
2021.43
"concept: 

an + an = 2 an

an × an = a2n

calculation: 

710 + 710 + 710 + 710 + 710 + 710 + 710  = 7n

7 × 710 = 7n

711 =  7n

∴ the required value of n is 11."
ee5d5e52be727cfff9c395586ebb4b29
2021.43
testbook.com
ee5d5e52be727cfff9c395586ebb4b29
"solve the following

(cos2 a - 1)(cot2 a + 1) + 1 = ?"
"solve the following

(cos2 a - 1)(cot2 a + 1) + 1"
testbook.com
2021.43
"formula used:

cosec2 a = 1 + cot2 a 

calculation:

according to the formula, we have

(cos2 a - 1)(cot2 a + 1) + 1 = (cos2 a - 1)(cosec2 a ) + 1 

⇒ (cos2 a × cosec2 a) - cosec2 a + 1

⇒ (cos2 asin2 a) - cosec2 a + 1

⇒ cot2 a - cosec2 a + 1

⇒ (-1) + 1 = 0

∴ the value of (cos2 a - 1)(cot2 a + 1) + 1 is 0."