Question

prove that √sec^2A+cosec^2A=tanA+cotA​

Answer 1

ANSWER:

METHOD 1:

√sec²A + cosec²A = tanA + cotA

Taking LHS

We know that

secA = 1/cosA

cosecA = 1/sinA

√1/cos²A + 1/sin²A

⟾ √sin²A + cos²A/cos²A.sin²A

Using

→ sin²A + cos²A = 1

⟾ √1/cos²A.sin²A

Using

→ √a/b = √a/√b

→ √a²b² = √(ab)² = ab

⟾ 1/cosA.sinA

Now, taking RHS

tanA + cotA

Using

→ tanA = sinA/cosA

→ cotA = cosA/sinA

➭ sinA/cosA + cosA/sinA

➭ sin²A + cos²A/cosA.sinA

Using

→ sin²A + cos²A = 1

➭ 1/cosA.sinA

Taking RHS & comparing with LHS

1/cosA.sinA = 1/cosA.sinA

LHS = RHS

Hence, proved

METHOD 2:

√sec²A + cosec²A = tanA + cotA

Using

→ sec²A = 1 + tan²A

→ cosec²A = 1 + cot²A

Taking LHS

➳ √1 + tan²A + 1 + cot²A

➳ √2 + tan²A + cot²A

Using

tanAcotA = 1

➳ √tan²A + cot²A + 2tanA.cotA

It is in the form of (a + b)² = a² + b² + 2ab

➳ √(tanA + cotA)² = tanA + cotA

LHS = RHS

Hence, proved

Answer 2

Answer:

QUESTION:

What is the mass number of an atom with 6 protons and 8 neutrons?

Answer:

$\huge{ \boxed{ \bold{ \sf{14 \: amu}}}}$

Explanation:

✑ First, Let's explore about ATOMIC MASS :

↱ An atom consists of electrons , protons and neutrons. The mass of electron is extremely small and it is taken as a negligible mass compared to the mass of a proton or neutron. Thus , The atomic mass is defined as the sum of the number of protons and neutrons present in the nucleus of an atom of that element. If is also called atomic weight. It is denoted by A. The nucleus determines the mass of an atom, while the number of electrons determines the size of the atom of the element.

Mathematically,

Atomic mass = Number of protons + Number of neutrons

i.e $\boxed{ \sf{A = p^{ + } + n^{0}}}$

———————————————————————

✎ Now , Let's find the atomic mass of atom having 6 protons and 8 neutrons :

☞ Atomic mass = No. of protons + No. of neutrons

➵ Atomic mass = 6 + 8

➵ Atomic mass =$\boxed{ \sf{14 \: amu}}$

And we're done !

Hope I helped!

Have a wonderful day! ツ

~TheFadedGirL♡

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