Find the value ofsec2θ−tan2θcosec2θ−cot2θ−12sin45∘cos15∘2sin15∘cos45∘

(c) 2sin45∘cos15∘sinC+sinD=2sin(2C+D)cos(2C−D)∴2C+D=45∘ or C+D=90∘2C−D=15∘ or C−D=30∘Solving these two equations, we getC=60∘,D=30∘∴2sin45∘cos15∘=sin60∘+sin30∘=(23+1)(d) ApplysinC−sinD=2sin(2C−D)cos(2C+D)C=60∘ and D=30∘∴2sin15∘cos45∘=sin60∘−sin30∘=(23−1)

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Class 11

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Find the value of ^{2} - ^{2} {}^{2} - ^{2} -1 2 45^{} 15^

Question

Easy

Solving time: 2 mins

Find the value of
$sec^{2} θ - tan^{2} θ$
$cosec^{2} θ - cot^{2} θ - 1$
$2 sin 4 5^{\circ} cos 1 5^{\circ}$
$2 sin 1 5^{\circ} cos 4 5^{\circ}$

Views: 5,765 students

Updated on: Mar 16, 2023

Book:

Mechanics Volume 1 (DC Pandey)

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Find the value of

sec^{2} θ - tan^{2} θ

cosec^{2} θ - cot^{2} θ - 1

2 sin 4 5^{\circ} cos 1 5^{\circ}

2 sin 1 5^{\circ} cos 4 5^{\circ}

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

(c)

2 sin 4 5^{\circ} cos 1 5^{\circ}

sin C + sin D = 2 sin (\frac{C + D}{2}) cos (\frac{C - D}{2})

∴ \frac{C + D}{2} = 4 5^{\circ} or C + D = 9 0^{\circ}

\frac{C - D}{2} = 1 5^{\circ} or C - D = 3 0^{\circ}

Solving these two equations, we get

C = 6 0^{\circ}, D = 3 0^{\circ}

∴ 2 sin 4 5^{\circ} cos 1 5^{\circ} = sin 6 0^{\circ} + sin 3 0^{\circ}

= (\frac{3 + 1}{2})

(d) Apply

sin C - sin D = 2 sin (\frac{C - D}{2}) cos (\frac{C + D}{2})

C = 6 0^{\circ}

and

D = 3 0^{\circ}

∴ 2 sin 1 5^{\circ} cos 4 5^{\circ} = sin 6 0^{\circ} - sin 3 0^{\circ}

= (\frac{3 - 1}{2})

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Question Text	Find the value of $sec^{2} θ - tan^{2} θ$ $cosec^{2} θ - cot^{2} θ - 1$ $2 sin 4 5^{\circ} cos 1 5^{\circ}$ $2 sin 1 5^{\circ} cos 4 5^{\circ}$
Updated On	Mar 16, 2023
Topic	Units and Measurements
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 4
Upvotes	451
Avg. Video Duration	6 min

Find the value of
$sec^{2} θ - tan^{2} θ$
$cosec^{2} θ - cot^{2} θ - 1$
$2 sin 4 5^{\circ} cos 1 5^{\circ}$
$2 sin 1 5^{\circ} cos 4 5^{\circ}$

Text solutionVerified

Filo tutor solutions (4)

Practice questions from Mechanics Volume 1 (DC Pandey)

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Practice questions on similar concepts asked by Filo students

Find the value ofsec2θ−tan2θcosec2θ−cot2θ−12sin45∘cos15∘2sin15∘cos45∘

Text solutionVerified

Filo tutor solutions (4)

Practice questions from Mechanics Volume 1 (DC Pandey)

Practice more questions from Units and Measurements

Practice questions on similar concepts asked by Filo students

Related books for questions on Units and Measurements

Find the value of
$sec^{2} θ - tan^{2} θ$
$cosec^{2} θ - cot^{2} θ - 1$
$2 sin 4 5^{\circ} cos 1 5^{\circ}$
$2 sin 1 5^{\circ} cos 4 5^{\circ}$