Question

$\sqrt{2}$ sinA = 1, find the value of sec²A - cosec²A

Answer 1

Given

→ √2 sinA = 1

→ sinA = 1/√2

→ sin 45° = 1/√2

→ A = 45°

Solution

→ sec²A - cosec²A

→ (secA + cosecA)(secA - cosecA)

→ (sec 45° + cosec 45°)(sec 45° - cosec 45°)

• sec 45° = cosec 45° = √2

→ (√2 + √2)(√2 - √2)

→ 2√2 × 0

→ 0

Hence required answer is 0.

Answer 2

Step-by-step explanation:

$\sqrt{2} \sin(a) = 1 \\ \\ \sec {}^{2} (a) - cosec {}^{2} (a)$

Now

$\sin(a) = \frac{1}{ \sqrt{2} }$

Now Trignometry Ration of sin =1/√2=45°

Sin(a)=1/√2

a=45°

Now

sec²(a)-cosec²(a)

Putting Value of a =45°

sec²(45)-cosec²(45)

Now

Trignometry Ratio for Sec 45=√2

Trignometry Ratio for cosec 45=√2

Now given

sec ²45-cosec² 45

√2²-√2²

=2-2

=0

$\mathbf{ \huge { \red{ \sec ^{2} (a) - cosec ^{2} (a) = 1}}}$