AKUEB HSSC-I Mathematics Trigonometric Identities MCQs & Practice Questions

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.1 Fundamental Law of Trigonometry / 8.1.4

AKU-EB Model Paper 2025MEDIUM

Fill in the blanks:

Show that

\cos(\alpha+\beta)\times\cos(\alpha-\beta)=1-(\sin^2\alpha+\sin^2\beta)

.
We will apply formula
That will give us
Rewriting further gives us, which expands and simplifies to

1-(\sin^2\alpha+\sin^2\beta)

, as required.

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.2 Trigonometric Ratios of Allied Angles / 8.2.2

AKU-EB Model Paper 2025MEDIUM

Fill in the blanks:

Using the fundamental law of trigonometry, prove

\cos\left(\dfrac{\pi}{2}+\alpha\right)=-\sin\alpha

.
We will apply formula
That will give us
Substitutingandgives the answer.

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.2 Trigonometric Ratios of Allied Angles / 8.2.3

AKU-EB Model Paper 2025HARD

The expression $5\sin\theta+12\cos\theta$ can be converted as

13\sin\left(\theta+\tan^{-1}\left(\dfrac{5}{12}\right)\right)

13\sin\left(\theta+\tan^{-1}\left(\dfrac{12}{5}\right)\right)

17\sin\left(\theta+\tan^{-1}\left(\dfrac{5}{12}\right)\right)

17\sin\left(\theta+\tan^{-1}\left(\dfrac{12}{5}\right)\right)

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.2 Trigonometric Ratios of Allied Angles / 8.2.1

AKU-EB Model Paper 2025EASY

The sum or difference of two angles is zero degrees or an integral multiple of $90$ degrees. The given condition is defined as

half anglesallied anglesdouble anglesadjacent angles

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.1 Fundamental Law of Trigonometry / 8.1.4

AKU-EB Model Paper 2025HARD

If $\tan\theta=2$ and $\theta$ lies in the third quadrant, then the value of $\cos\theta$ will be equal to

\dfrac{\sqrt5}{5}

\dfrac{5}{\sqrt5}

-\dfrac{5}{\sqrt5}

-\dfrac{\sqrt5}{5}

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.3 Double, Half and Triple Angle Identities / 8.3.1

AKU-EB Model Paper 2025EASY

If $\sin\alpha=a$ and $\cos\alpha=b$ , then the value of $\sin2\alpha$ will be equal to

ab

\dfrac{a}{b}

\dfrac{2a}{b}

2ab

Class 11 - Mathematics / Unit 8 - Trigonometric Identities / 8.4 Sum/Difference and Product of Sine and Cosine / 8.4.1

AKU-EB Model Paper 2025MEDIUM

$\sin\alpha+\sin2\beta$ is equal to

\cos\dfrac{\alpha+2\beta}{2}\sin\dfrac{\alpha-2\beta}{2}

\sin\dfrac{\alpha+2\beta}{2}\cos\dfrac{\alpha-2\beta}{2}

2\cos\dfrac{\alpha+2\beta}{2}\sin\dfrac{\alpha-2\beta}{2}

2\sin\dfrac{\alpha+2\beta}{2}\cos\dfrac{\alpha-2\beta}{2}

Trigonometric Identities - HSSC-I Mathematics