Question

The value of cosec (75° + theta ) -sec(15°-theta) -tan ( 55° + theta ) +cot (35° - theta) = ?

please help me friends ​

Answer 1

Answer:

0

Step-by-step explanation:

From properties of trigonometry:

secA = cosec(90 - A)

cotA = tan(90 - A)

Therefore,

• sec(15 - ∅) = cosec(90 - (15 - ∅))

= cosec(90 - 15 + ∅)

= cosec(75 + ∅)

→ sec(15 - ∅) = cosec(75 + ∅)

• cot(35 - ∅) = tan(90 - (35 - ∅))

= tan(90 - 35 + ∅)

→ cot(35 - ∅) = tan(55 + ∅)

Therefore,

→ cosec(75 + ∅) - sec(15 - ∅) - tan(55 + ∅) + cot(35 - ∅)

→ cosec(75 + ∅) - cosec(75 + ∅) - tan(55 + ∅) + tan(55 + ∅)

→ 0

Answer 2

$\cosec(75 \degree + \theta) - \sec(15 \degree - \theta) - \tan(55 \degree + \theta) + \cot(35 \degree - \theta)$

$= \cosec(90 \degree - (15 \degree - \theta) ) - \sec(15 \degree - \theta) - \tan(90 \degree - (35 \degree - \theta)) - \cot(35 \degree - \theta)$

$= \sec(15 \degree - \theta) - \sec(15 \degree - \theta) - \cot(35 \degree - \theta) + \cot(35 \degree - \theta)$

$= 0 + 0$

$= 0$