Question

(tan theta / sec theta - 1) + (tan theta / sec theta + 1) is equal to

(a) 2 tan theta
(b) 2 sec theta
(c) 2 cosec theta
(d) 2 tan theta sec theta ​

Answer 1

Answer:

(d) 2tan theta sec theta is the right answer

Answer 2

Step-by-step explanation:

→ (tanØ/secØ -1) + (tanØ/secØ + 1)

→ tanØ [(secØ + 1 + secØ - 1)/(secØ - 1)(secØ + 1)]

Used identi: a + b)(a - b) = a² - b²

→ tanØ (2secØ)/(sec²Ø - 1)

We know that, sec²Ø - 1 = tan²Ø

→ tanØ (2secØ)/(tan²Ø)

→ 2 secØ/tanØ

Also, secØ = 1/cosØ, tanØ = sinØ/cosØ

Substitute the values,

→ 2 × (1/cosØ)/(sinØ/cosØ)

→ 2 × 1/sinØ

→ 2 cosecØ

Hence, option c) 2 cosecØ is correct.