Tan2-cot2-2-sec2-cosec2-

nbsp;We know that, 1 + tan^2θ = sec^2θ .....(1) and 1 + cot^2θ = cosec^2θ .....(2) Adding (1) and (2), 2 + nbsp;tan^2θ + cot^2θ = nbsp;sec^2θ + co ...

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Byju's Answer

Standard X

Mathematics

Trigonometric Identities

tan2θ+cot2θ+2...

Question

$t a n^{2} θ + c o t^{2} θ + 2 = s e c^{2} θ + c o s e c^{2} θ$

True

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False

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Solution

The correct option is A True
We know that, $1 + t a n^{2} θ = s e c^{2} θ . . . . . (1) and 1 + c o t^{2} θ = c o s e c^{2} θ . . . . . (2) Adding (1) a n d (2), 2 + t a n^{2} θ + c o t^{2} θ = s e c^{2} θ + c o s e c^{2} θ$
Hence, the given statement is true.

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Similar questions

Q. Prove that :

\frac{t a n θ - c o t θ}{s i n θ c o s θ} = s e c^{2} θ - c o s e c^{2} θ = t a n^{2} θ - c o t^{2} θ

Q. Choose the correct answer from the alternatives given.
If

0 < θ < 90^{\circ}

then what is the minimum value of

s i n^{2} θ + c o s^{2} θ + t a n^{2} θ + c o t^{2} θ + s e c^{2} θ + + c o s e c^{2} θ

Q. In

Δ A C B

right-angled at B, if AB =3 units, BC = 4units and

∠ A C B = θ,

then the value of

[c o s e c^{2} θ - t a n^{2} θ + c o s^{2} θ + s e c^{2} θ - c o t^{2} θ + 2 - (- s i n^{2} θ)] i s e q u a l t o

Q. If θ is an acute angel such that

s e c^{2} θ = 3,

then find the value of

\frac{{tan}^{2} θ - c o s e c^{2} θ}{{tan}^{2} θ + c o s e c^{2} θ}

Prove:

s e c^{2} θ + c o s e c^{2} θ = s e c^{2} θ \times c o s e c^{2} θ

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tan2θ+cot2θ+2=sec2θ+cosec2θ

The correct option is A True We know that, 1+tan2θ=sec2θ.....(1) and1+cot2θ=cosec2θ.....(2)Adding (1) and (2),2+tan2θ+cot2θ=sec2θ+cosec2θ Hence, the given statement is true.

$t a n^{2} θ + c o t^{2} θ + 2 = s e c^{2} θ + c o s e c^{2} θ$

The correct option is A True
We know that, $1 + t a n^{2} θ = s e c^{2} θ . . . . . (1) and 1 + c o t^{2} θ = c o s e c^{2} θ . . . . . (2) Adding (1) a n d (2), 2 + t a n^{2} θ + c o t^{2} θ = s e c^{2} θ + c o s e c^{2} θ$
Hence, the given statement is true.